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NEW TREATISE

USE OF THE GLOBES;

OR,

A PHILOSOPHICAL VIEW

i OP r^

THE EARTH AND HEAVENS:

COMPREHENDING

AN ACCOUNT OF THE FIGURE, MAGNITUDE, AND MOTION OF THE EARTH ;
WITH THE NATURAL CHANGES OF ITS SURFACE, CAUSED BY FLOODS,
EARTHQUAKES, ETC. TOGETHER WITH THE PRINCIPLES OF METEOROLOGY
AND ASTRONOMY; WITH THE THEORY OF THE TIDES, ETC.

PRECEDED BY
AN EXTENSIVE SELECTION OF ASTRONOMICAL AND OTHER DEFINITIONS;

AND ILLUSTRATED BY A GREAT VARIETY OF PROBLEMS,
QUESTIONS FOR THE EXAMINATION OF THE STUDENT, ETC. ETC.

DESIGNED FOR THE INSTRUCTION OF YOUTH.

BY THOMAS KEITH,

BY J. KOWBOTHAM, F.E.A.S.

AUTHOR OF " A NEW DERIVATIVE DICTIONARY," ETC.

LONDON:

PRINTED FOR

LONGMAN, BROWN, GREEN, AND LONGMANS,

PATERNOSTER-ROW.

1844.

LONDON :

Printed by A. SPOTTISWOODB,
New- Street- Square.

PREFACE

TO THE PRESENT EDITION.

ALTHOUGH the Treatise on the Globes by Mr. Keith
stands pre-eminent, in point of merit, to any other
work of the same kind ; it is, nevertheless, necessary,
from the nature of many of the problems, that they
should, from time to time, be altered, in order to
make them correspond, as nearly as possible, with
the positions of the heavenly bodies, for present or
future periods, as given in the Nautical Almanacs.

In order to render this Edition more acceptable
and interesting than the former ones, the Editor has
not only introduced many new questions relating to
the positions of the sun, moon, and planets for the
years 1843, 1844, 1845, and 1846, respectively ; but
has also corrected various errors that had inadvert-
ently escaped the notice both of himself and a former
editor, who made many important alterations and
improvements in the last edition but one, of which
his own Preface, which follows, will explain the par-
ticulars.

J. EOWBOTHAM, F.E.A.S.

55. Queen's Row,
Walworth, 1843.

A 2

PREFACE

TO THE PRECEDING EDITION,

THOUGH fully aware that several parts of Mr. Keith's
" Treatise on the Use of the Globes' were susceptible
of a more scientific arrangement, the Editor has made no
innovations upon the original plan of the Author, but has
rather endeavoured to introduce such improvements in
this Edition as were consistent with that plan ; and to
adapt the work to the present improved state of science,
without compromising its identity by disturbing the gene-
ral arrangement.

The following are a few of the principal alterations and
improvements of this Edition : the Definitions in Part L,
which were, in many respects, very defective, have under-
gone a careful revision. The very incorrect and'obscure
illustration of the earth's diurnal motion (chap. 4.) has
been removed, and arguments demonstrative of the truth
of the hypothesis substituted in its room. Many very
important alterations have also been made in Part II.,
particularly in Chapters 5, 6, and 7- To this part of
the work, a tabular view of the principal elements of the
Planets has been added, and a more useful table of the
Moon's age (copied from Mackay's Navigation) has been
substituted for that given by Mr. Keith. The Problems
in Part III. have been carefully revised and corrected,
and the solutions of such as are performed by the as-
sistance of the Nautical Almanac have been adapted to
the recent improvements in that work. To this Edition a
great number of original notes, and an etymological table
of the principal scientific terms made use of in the work,
have been added : the value of the former, the Editor pre-
sumes, will be duly appreciated; the latter is a novelty,
tihty of which needs no comment. That nothing
might be omitted which could tend to secure for the work

PREFACE TO THE PRECEDING EDITION'. V

a continuance of that extensive patronage it has hitherto
experienced, a new plate of the full moon (copied ex-
pressly for this purpose from the Editor's Astronomicon),
has been introduced, with references to the names and
situations of all the principal spots on the lunar disc.*
In short, while the utmost care has been taken to expunge
what was superfluous, no pains have been spared to sup-
ply all that was deficient. To those, therefore, who, not
satisfied with being enabled merely to work the problems
on the Globes, are desirous of attaining a scientific know-
ledge of their use in illustrating some of the leading prin-
ciples of Geography and Astronomy, the Editor trusts he
may, with confidence, say, in the words of Horace, " Quod
petis, hie est."

64. Crawford Street, Bryanstone Square,
February 21. 1834.

*#* A KEY (by the Editor) is also published, comprising
the ANSWERS to the PROBLEMS in " The Treatise on
the Use of the Globes" To be had separately, or
bound up with the work, t

* See Prior's Lectures on Astronomy, illustrated by the Astrono-
micon.

f The Key, to which the above note refers, has been re-edited
by Mr. Rowbotham, who has adapted it to the present edition.

A 3

ORIGINAL PREFACE.

AMONGST the various branches of science studied in our
academies, and places of public education, there are few
of greater importance than that of the Use of the Globes.
The earth is our destined habitation, and the heavenly
bodies measure our days and years by their various revo-
lutions. Without some acquaintance with the different
tracts of land, the oceans, seas, &c. on the surface of the
terrestrial globe, no intercourse could be carried on with
the inhabitants of distant regions, and consequently their
manners, customs, &c. would be totally unknown to us.
Though the different tracts of land, &c, cannot be so mi-
nutely described on the surface of a terrestrial globe as on
different maps ; yet the globe shews the figure of the earth,
and the relative situations of the principal places on its
surface, more correctly than a map. Had the ancients
paid no attention to the motions of the heavenly bodies,
historical facts would have been given without dates, and
we should have had neither dials, clocks, nor watches.
To the celestial observations of Eudoxus, Hipparchus, &c.
we are indebted for the knowledge of the precession of
the equinoxes. Without some acquaintance with the celes-
tial bodies, our ideas of the power and wisdom of the
Creator would be greatly circumscribed and confined.
The learned and pious Dr. Watts observes, " What won-
" ders of Wisdom are seen in the exact regularity of the
" revolutions of the heavenly bodies I Nor was there ever
" any thing that has contributed to enlarge my apprehe»-
" sions of the immense power of God, the magnificence

PREFACE. Vll

« of his creation, and his own transcendent grandeur, so
" much as the little portion of astronomy which I have
" been able to attain. And I would not only recommend
" it to young students, for the same purposes, but I would
" persuade all mankind, if it were possible, to gain some
" degree of acquaintance with the vastness, the distances
" and the motions of the planetary worlds, on the same
" account."

Dr. Young, in his Night Thoughts, says,
" An undevout astronomer is mad."

There is scarcely a writer on the different branches of
education who has not expressly recommended the study
of the globes. Milton observes, that " ere half the school
" authors be read, it will be seasonable for youth to learn
« the use of the globes." Yet, notwithstanding the im-
portance of the subject, it is entirely neglected in our
public schools : and in many of our private academies it
has been frequently imperfectly taught ; probably for want
of a treatise sufficiently comprehensive in its object, and
illustrated by a suitable number of examples.

There are several treatises on the globes extant, but
they have been chiefly written by mathematical instru-
ment-makers *, or by teachers unacquainted with mathe-

* The principal globe-makers in London, are CARY, BARDIX, NEW-
TON, and ADDISOK.

CART'S globes are 21, 18, 15, 12, 9, and 6 inches in diameter, and
the celestial globe may be purchased either with or without the hiero-
glyphical figures depicted on the surface.

BARDIN'S globes, or as they are usually called, the NEW BRITISH
GLOBES, are 18 inches, and 12 inches in diameter. — The NEW BRI-
TISH GLOBES, manufactured under the direction of Messrs. W. and S.
Janes, Holborn, are particularly recommended by Mr. Vince, in vol. i.
page 569. of his complete System of Astronomy, and were introduced
into the Royal Observatory at Greenwich, by the late Dr. Maskelyne.

NEWTON'S globes are 15 inches, and 12 inches in diameter. The
horizon on these globes is the same as on Bardin's ; only, instead of the
signs of the zodiac, the ecliptic and zodiacal constellations are intro-

vifi PREFACE.

matics. The works of the former must be defective, for
want of practice in the art of teaching ; and many of the
productions of the latter are too puerile and trifling to be
introduced into a respectable academy. Youth learn no-
thing effectually, but by frequent repetition ; a multiplicity
of examples therefore becomes absolutely necessary ; but
these examples should be so varied, and the mode of pro-
posing the questions so diversified, as to give the scholar
room for the exertion of his faculties, or otherwise no im-
pression will remain on his mind. Treatises on the globes
are generally either without any practical exercises ; or
the exercises are so similar, that when the pupil has finish-
ed one of them, the rest may be performed without the
trouble of thinking. Examples of this kind may serve to
pass away the time, but they will never instruct the
scholar.

Had any mathematical writer of note furnished the
student with a treatise on the globes, the following work
would probably have never appeared ; but it rarely happens
that the man of science, whose whole time is employed
in abstruse researches, will stoop to the humble task of ac-

duced. The analemma on the surface is not essentially different from
that on Cary's globes.

ADBISON'S globes are 18, 12, and 10 inches in diameter. The ana-
lemma on the surface of these globes is the same as the analemma on
Cary's globes. Mr. Addison has constructed a superb pair of globes,
86 inches in diameter, price 60 guineas ;
or separate, -f the Aqueous, 35 guineas,
L — celestial - 30 guineas.

General Prices of Globes.
21 inches in diameter, from 10 to 19 guineas, Gary.

' ' ' - ~ 8 to 16--. Gary, Bardin, Addison.

6 to 12 - - - Newton, Gary.
12 - - . . 3ito6- - fCary,Bardin, Newton,

\Addison.

3 to 5 - - - Addison.
3 to 4$- - -Gary.
• " - - 2| to ^3 18s. Gary.

PREFACE. IX

commodating himself to the capacity of a learner. To a
man in the habit of contemplating the writings of a New-
ton, or travelling in the dry and difficult paths of abstract
knowledge, a treatise on the globes is a mere plaything, a
trifle not worth notice; as at one glance he sees and compre-
hends every problem that can be performed by them.
Such a man would acquire no credit by writing a Treatise
on the Globes ; for, notwithstanding the utility of the sub-
ject, its simplicity would leave no room for him to display
his abilities : the task, therefore, necessarily devolves on
writers of a more humble rank.

The ensuing Treatise has been formed entirely from
the practice of Instruction, and is arranged in the follow-
ing order :

PART I. c The definitions are very extensive, and, it is
hoped, sufficiently plain and clear. Where the name of
any ancient author occurs, the time in which he flourished,
and his country, are generally mentioned in a note ; this
practice is followed throughout the book. The table of
climates has been newly calculated, and the principle of
calculation is given at full length. The first chapter like-
wise contains a table of the constellations, with the fabu-
lous history of several of them : the Greek alphabet, &c.
If the definitions, geographical theorems, &c. in this chapter
be well explained by the tutor, it is presumed that the
scholar will derive considerable advantage. The second
chapter contains the general properties of matter, and the
laws of motion, as preparatory to the reading of the third
and fourth chapters ; which would otherwise be less intel-
ligible. To the third and fourth chapters are added some
useful notes, which ought to be attended to by those stu-
dents who are acquainted with arithmetic. The fifth
chapter treats of springs, rivers, and the saltness of the sea,
the sixth of the tides ; and the seventh of earthquakes, &G
with their effects and causes. The subject of the eighth
A 5

PREFACE.

chapter is the atmosphere, and of the ninth, meteorology.
From each of these chapters, it is hoped, the student will
derive some useful information.

It has not been usual to introduce several of the afore-
said subjects into a Treatise on the Globes. An intelli-
gent reader will, however, readily admit them to be less
extraneous, equally entertaining, and more instructive than
scraps of poetry, historical anecdotes, &c. with which some
of our Treatises on the Globes abound. Poetical scraps
seldom elucidate either mathematical or philosophical sub-
jects, and generally divert the attention of the student
from the main object of his pursuit.

PART II. This part comprehends the elementary prin-
ciples of Astronomy, including an account of the solar
system. These ought to be clearly understood by the
young student before he attempts to solve many of the
problems in the succeeding parts of the book. The object
in learning the Use of the Globes should be to illustrate
some of the most important branches of geography and
astronomy ; and this object cannot be attained by merely
twirling the globe round and working a few problems, with-
out understanding the principles on which their solutions
are founded. Lessons thoroughly explained and clearly
understood make a lasting impression on the student's me-
mory, and will enable him, not only to solve such problems
as he may meet with in books on the Globes, but to frame
several new problems himself, and to solve others which
he never heard of before.

In the notes attached to this part of the following work,
the distances, magnitudes, &c. of the planets are all accu-
rately calculated. This laborious task the author would
gladly have avoided, but he found the accounts of the dis-
tances, magnitudes, &c. of the planets so variable and con.
ictory, even in astronomical works of repute, and
frequently m the same author, that he conceived such

PREFACE. XI

notes as he has introduced would be very useful to a
learner.

PART III. contains an extensive collection of Prob-
lems ; illustrated by a great number of useful examples,
many of which are elucidated with notes of considerable
importance.

PART IV. comprehends a miscellaneous selection of
Problems, and Questions for the examination of the stu-
dent. These questions will be found very useful, and
may be extended with advantage by the tutor.

To CONCLUDE. The author apprehends that he has
omitted nothing of importance that particularly relates to
the subject, and he hopes, at the same time, that this
work will be found to contain little or no extraneous
matter. He has endeavoured to supply the young student
with a Treatise on the Globes, which may not be unworthy
of attention, as a work of science, yet sufficiently plain and
intelligible. To those who may object to the smallness of
the type, and the closeness of the printing, the author has
to observe, that had the work been printed on a larger
type, it would have made an octavo volume consisting of
at least six hundred pages ; the purposes for which it is
designed would have been completely defeated ; the price
doubled ; and the book, from its size, rendered less con-
venient and useful.

A NEW plate has been delineated for this work, by J,
Rowbotham, F. R. A. S., showing the path of the planet
Jupiter in the Zodiac, for the years 1845 and 1846, which
will likewise nearly correspond to the years 1866 and 1867
to 1868, together with the constellations and principal
stars through and near which he passes, agreeably to their
appearance in the heavens. Delineations of this kind will
A 6

xii PREFACE.

not only prove amusing, but instructive to the scholar, as
they give a more correct idea of the relative situations of
the stars than a globe.

By laying down on paper all the principal constellations
from the celestial globe, or from a catalogue of stars, as
directed in Problem CIL, rejecting such stars as are
smaller than those of the sixth magnitude, and those con-
stellations which do not come above the horizon, the
young student will soon render the* appearance of the
heavens familiar to him.

The whole of this edition has been carefully revised, and
a considerable quantity of new matter has been intro-
duced, with a view of rendering it as complete, and com-
prehensive, as the nature of the subject will admit.

J. ROWBOTHAM, F. R. A. S.
WALWORTH, January 1. 1843.

THE CONTENTS.

PART I.

CHAP. I. LINES ON THE ARTIFICIAL GLOBES, ASTRONOMICAL DEFI-

NITIONS, GEOGRAPHICAL THEOREMS, &c. Pages 1 to 46

Aberration - (JDef. 122) Page 41

Cameleopardalus Def. Page 31

Acronical - (90) - 26

Cams Major 34

Almacantars - (40) - 11

Canis Minor 35

Altitude - (45) - 11

Celestial Globe (2) - 1

Amplitude - (48) - 12

Cepheus - - 31

Amphiscii - (74) - 20

Centrifugal Force (124) - 42

Andromeda SO

Centripetal Force (123) - 42

Angle of Position (87) - 25

Cerberus - - - - 31

Antartic Pole (4) - 2

Cetus ... 35

Antinous - ^ ., - - ^ 30

Centaurus - 35

Antipodes - (79) - 21

Chimboraso Mountain (note) 59

Antoeci - - (77) - 21

Circles, Great (6) - 3

Aphelion - -(111) - 40

Circles, Small - (7) - 3

Apogee - - (109) - 40

Climate (69) Tables of - 18

Apparent noon - (53) - 13

Colures - (14) - 5

Apsides - - (113) - 4O

Coma Berenices 32

Aquila - 30

Compass, Mariner's (33) - 9

Ara - 34

Constellation - (91) 26, 124

Arctic Pole - (4) - 2

Constellations, a Table of, 27 to 29

Argo Navis 34

Constellations, Historical

Ascension, Right (80) - 21

Account of - - 29 to 36

Ascension, Oblique (81) - 21

Cor Caroli - 32

Ascensional Difference (83) 21

Corvus - 35

Asscii - - (74) - 20

Corona Borealis 32

Aspect of the planets (101) 39

Cosmical - (93) - 26

Asterion et Chara 30

Crepusculum - (84) - 21

Auriga - , - 129

Crux - 35

Azimuth - - (49) - 12

Culminating Point (52) - 13

Azimuth, or Vertical Cir-

Cygnus - - 32

cles - - (43) - 11

Axis of the Earth - (3) - 2

Day, Astronomical (58) - 14

Artificial - (59) - 14

Bayer's Characters of the

Civil - - (60) - 14

Stars - - (94) - 37

True Solar - (56) - 13

Bootes - - - 31

Mean Solar (57) - 13

Brazen Meridian - • r. •• '.,9

Siderial - (61) - 14

Declination - (15) - &

Canes Venatici 30
Cardinal Points (24, 25, 26) 7 & 8

Degree, length of, (note) - Ctf
Delphinus 82

Cassiopeia - . 31

Descensional Difference (83) 21

CONTENTS.

Digit
Direct
Disc -
Diurnal Arc -
Divisibility
Draco

Def.
(105)
(102)
(106
(120)

Page
39
39
39
41
47
32

Eccentricity - (114) - - 40

Eclipse of the Sun ( 1 1 7) - 40

Eclipse of the Moon( 11 8) - 40

Ecliptic - - (11) - 3

Ellipsis (note) - - - 59

Elongation - (119) 40, 172

Equator - - (10) - " 3

Equation of Time (55) - 13

Equinoctial Points (30) - 8

Equulus - - 32

Eridanus - - 35

Extension - 47

Eudoxus (note) - - 16

Figure - 47
Fixed Stars - (89) 25 & 133

Foci of an Ellipsis (note) - 60

Force - - . -49

Force, Centrifugal (124) - 42

Force, Centripetal (123) - 42

Galaxy - - (92) - 36

Geocentric - (107) - 40

Geographical Theorems - 42

Globe, Celestial - (2) - 1

Globe, Terrestrial (1) - 1

Gravity 48

Great Circles - (6) - 3

Greek Alphabet - - 38

Heliacal - (90) - 26

Heliocentric - (108) - 40

Hemisphere - (32) - 8

Hercules 32

Hesiod(note) - - - 16

Heterocii - (75) - 20
Himalaya Mountains

(note) - - .59, 90

Hipparchus (note) - 5,15
Historical Account of the

Zodiacal Signs, &c. 29 to 36

Horizon (20, 21, 22) - 6, 7

Horizon, wooden (23) - 7

Hour Circle - (19) - 6

Hour Circles -
Hydra -

Inertia -

Def. Page
(50) - IS T
35

- 48

Lacerta - 32

Latitude of a place '(35) - 10
Latitude of aPlanet or Star (36)10
Leo Minor - - .32

Lepus - - 35

Line of the Apsides (113) - 4O

Lines of Longitudes (8) - 3

Longitude of a place (38) - 10
Longitude of a planet or

Star - - (39) - 11

Lynx 33

Lyra - - - - 33

Mariner's Compass (33 & 34) 9
Matter, General Proper-
ties of, &c. - - - 46
Meridians - (8) - 3
Meridian, Brazen (5) - 2
Meridian, First - (9) - 3
Microscopium - 35
Milky Way - (92) - 36
Mobility - - - - 47
Mons Maenalus - 33
Monoceros 36
Motion, Absolute, &c. - 49
Motion, General Laws of - 49
Motion, Compound, &c. - 51

Nadir - - (28) - 8

Nebulous Stars (93) - 37

New South Shetland (note) 78

Nocturnal Arc (121) - 41

Nodes of a Planet (100) - 39

Noon, Apparent (53) - 13

Noon, True or Mean (54) - - 13

Oblique Ascension (81) - 21

Oblique Descension (82) - 21

Occultation - (115) - 40

Orbit of a Planet (99) - 39

Orion 36

Parallax - - (86) - 24
Parallels of Celestial Lati-
tude - - (41) - 11
Parallels of Declination (42) 11

CONTENTS.

Def. Page

Parallels of Latitude (18)- 6
Pegasus - S3

Pendulum, vibrating se-
conds, (note) - - 60
Perigee - (110) - 40
Perihelion - (112) - 40
Periceci - - (78) - 21
Periscii - - (76) - 20
Perseus 33

Piscis Australis 36

Planets - (95, 96, 97, 98) 38, 39
Pliny (note) - 16

Poetical rising and setting

of the Stars - (90) - 26
Points, Cardinal (24, 25, 26) 7, 8
Polar Axis of the Earth (note) 61
Polar Circles - (17) - 5
Polar Distance - (47) - 12
Polar star (note) - 2, 132, 133
Poles of the Earth - (4) - 2
Pole of any Circle (29) - 8
Positions of the Sphere (65) 16
Precession of the Equi-
noxes - - (64) - 15
Prime Vertical - (44) - 11

Quadrant of Altitude (37) - 10

Refraction - (85) - 22

Retrograde - (104) - 39

Rhumbs - (88) - 25

Right Ascension - (80) - 21

Robur Caroli - 36

Sagitta - ^34

Scutum Sobieski 34

Def. Page

Serpens - - - - 34

Serpentarius - . 34

Sextans ... 35

Six o'clock Hour Line (51) 12

Small Circles - (7) - 3

Solidity - - - - 47

Solstitial Points (31) - 8
Sphere, Positions of (65,

66, 67, 68) - 16, 17, & 217

Spheroid (note) 59

Stationary - (103) - 39

Taurus Poniatowski -

Triangulum

Transit

Tropics -
Twilight

(116) -
(16) -

(84) -

34
34
40
5
21

Variation of the Compass (34) 9

Velocity - - - 49

Vertical Circles - (43) - 11

ViaLactea - (92) - 36

Vulpecula et Anser - 34

Ursa Major -

34, 131

Year, Sidereal - (63) - 15
Year, Solar - (62) - 15

Zenith - - (27) - 8
Zenith Distance (46) -.11
Zodiac - - (12) - 4
Zodiacal Signs, (13) page
4 ; Historical Account
thereof - - - 29 & 30
Zones (70, 71, 72, 73) 19, 20

CHAP. II. Of the general Properties of Matter and the Laws

of Motion - - - - -46

III. Of the Figure of the Earth and its Magnitude - 57

IV. Of the Diurnal and Annual Motion of the Earth - 64
V. Of the Origin of Springs and Rivers, and of the

Saltness of the Sea - - - - - 73

VI. Of the Flux and Reflux of the Tides - - 78
VII. Of the natural Changes of the Earth, caused by

Mountains, Floods, Volcanoes, and Earthquakes - 8f)

VIII. Of the Atmosphere, Air, Winds, and Hurricanes - 101

IX. Of Vapours, Fogs, Mists, Clouds, Dew, &c. - 110

1. Vapours - - 110

2. Fogs and Mists - - - - HO

3. Clouds - - - 110

XVl CONTENTS.

Page

4. Dew - ... - - 111

5. Rain - - - - --111

6. Snow and Hail - - - -113

7. Thunder and Lightning - - 1 13

8. The Falling Stars 114

9. Of the Ignis Fatuus - - 1 15

10. Of the Aurora Borealis - - - - 115

11. Of the Rainbow - - - - 116

PART II.

THE ELEMENTARY PRINCIPLES OF ASTRONOMY.

CHAP. I. The General Appearance of the Heavens - - 121
II. Of the Situation of the principal Constellations,
and the manner of distinguishing them from each
other - ; - 124

III. Of the Motion of the Fixed Stars by the Precession

of the Equinoxes, by Aberration, and by the Nuta-
tion of the Earth's Axis ; their proper Motions,
Distance, variable Appearance, &c. - - 133

IV. The Method of Measuring the Altitudes, Zenith,

Distances, &c. of the Heavenly Bodies, including
a Description of the Astronomical Quadrant, Cir-
cular and Transit Instrument - - - 138
V. Of the Solar System - - 141

1. Of the Sun - - - - 141

2. Of Mercury - 142

3. OfYenus - . 146

4. Of the Earth and the Moon - - - 149

5. Of Mars - - . - - 158

6. Of Vesta - - - 160

7. Of Juno - - - - - -160

8. Of Ceres - . - - - 160

9. Of Pallas . 161

10. Of Jupiter and his Satellites - - - 161

11. Of Saturn, his Satellites, and Ring - 166

12. Of the Georgium Sidus and its Satellites - 170
VI. On the Nature of Comets ; the Elongations, Sta-
tionary and Retrograde Appearances of the
Planets; and on the Eclipses of the Sun and
Moon ., , - . _ _ . i7i

1. On Comets - .... 171

2. Of the Elongations, &c. of the Interior Planets 172

3. Of the Stationary and Retrograde Appearances

of the Exterior Planets - - _ - 173

4. On Solar and Lunar Eclipses - . - 174
General Observations on Eclipses - - 176
Number of Eclipses in a Year - - - 177

CONTENTS. XVU

Page

VII. Of the Calendar - - - - 178

1. The Cycle of the Moon - - - 179

2. The Epact - - - 179

3. The Cycle of the Sun - - 180

4. The Number of Direction - - 181
.5. To find the Paschal Full Moon by the Epact - 182

6. Of the Year by the Gregorian Account - - 185
General View of the Planetary System 186 and 187

PART III.

PROBLEMS PERFORMED BY THE TERRESTRIAL GLOBE.
Preparatory Problem - - - 188

PROBLEM I. To find the latitude of any given place - 189

PROBLEM II. To find all those places which have the same

latitude as any given place - - - 190

PROBLEM III. To find the longitude of any place 190

PROBLEM IV. To find all those places that have the same

Longitude as any given place - - - - 191

PROBLEM V. To find the latitude and longitude of any

place - 191

PROBLEM VI. To find any place on the Globe, having the

latitude and longitude of that place given - 192

PROBLEM VII. To find the difference of latitude between

any two places - 193

PROBLEM VIII. To find the difference of longitude be-
tween any two places - - - - 193

PROBLEM IX. To find the distance between any two
places - - 194

PROBLEM X. A place being given on the Globe, to find
all places which are situated at the same distance from it
as any other given place - - - - 1 96

PROBLEM XI. Given the latitude of a place and its dis-
tance from a given place, to find that place whereof the
latitude is given - - - - - 197

PROBLEM XII. Given the longitude of a place, and its
distance from a given place, to find that place whereof the
longitude is given - - - - 198

PROBLEM XIII. To find how many Miles make a Degree

of longitude in any given parallel of latitude - - 199

PROBLEM XIV. To find the bearing of one place from
another ------ 200

PROBLEM XV. To find the Angle of Position between two

places ------- 201

PROBLEM XVI. To find the Antoeci, Periceci, and Anti-
podes to the inhabitants of any place - 204

PROBLEM XVII. To find at what rate per hour the Inha-

xviii CONTENTS.

Page

bitants of any given place are carried from West to East,
by the Revolution of the Earth on its Axis - - 205

PROBLEM XVIII. A particular place and the hour of the
day at that place being given, to find what hour it is at any
other place - 206

PROBLEM XIX. A particular place and the hour of the
day being given, to find all places on the Globe where it is
then noon, or any other given hour - - 207

PROBLEM XX. To find the Sun's longitude (commonly

called the Sun's place in the ecliptic) and its declination - 209

PROBLEM XXI. To place the Globe in the same situation
with respect to the Sun, as the Earth is at the Equinoxes
at the Summer Solstice, and at the Winter Solstice, and
thereby to show the comparative lengths of the longest and
shortest days - - - - - -211

PROBLEM XXII. To place the Globe in the same situation
with respect to the Polar Star in the Heavens, as the
Earth is to the inhabitants of the Equator, &c. viz. to
illustrate the three positions of the Sphere, Right, Parallel,
and Oblique, so as to show the comparative lengths of the
longest and shortest days - - - /- 217

PROBLEM XXIII. The month and day of the month being
given, to find all places of the Earth where the Sun is ver-
tical on that day ; those places where the Sun does not set,
and those places where he does not rise on the given day 222

PROBLEM XXIV. A place being given in the Torrid Zone,
to find those two days of the year on which the Sun will
be vertical at that place - 224

PROBLEM XXV. The month and day of the month being
given (at anyplace not in the Frigid Zones), to find what
other day of the year is of the same length - - 225

PROBLEM XXVI. The month, day, and hour of the day

being given, to find where the sun is vertical at that instant 226

PROBLEM XXVII. The month, day, and hour of the day
at any place being given, to find all those places of the
Earth where the Sun is rising, those places where the sun is
setting, those places that have noon, that particular place
where the Sun is vertical, those places that have morniug
twilight, those places that have evening twilight, and those
places that have midnight - 227

PROBLEM XXVIII. To find the time of the Sun's rising
and setting, and the length of the day and night at any
place not in the Frigid Zones - 229

PROBLEM XXIX. The length of the day at any place, not
in the Frigid Zones, being given, to find the Sun's declin-
ation, and the day of the month - « - 231
PROBLEM XXX. To find the length of the longest day at
any place in the North Frigid Zone - - - 233

CONTENTS. Xix

Page

PROBLEM XXXI. To find the length of the longest night

at any place in the North Frigid Zone - 234

PROBLEM XXXII. To find the number of- days which the

Sun rises and sets at any place in the North Frigid Zone 235

PROBLEM XXXIII. To find in what degree of north lati-
tude on any day between the 21st of March and the 21st
of June, or in what degree of south latitude, on any day
between the 23d of September and the 21st of December,
the Sun begins to shine constantly without setting ; and
also in what latitude in the opposite hemisphere he begins
to be totally absent ----- 237

PROBLEM XXXIV. Any number of days, not exceeding
182, being given, to find the parallel of north latitude in
which the Sun does not set for that time - - 238

PROBLEM XXXV. To find the beginning, end, and dura-
tion of twilight at any place on any given day - - 239

PROBLEM XXXVI. To find the beginning, end, and du-
ration of constant day -or twilight at any place - - 241

PROBLEM XXXVII. To find the duration of twilight at

the North Pole - - 242

PROBLEM XXXVIII. To find in what Climate any given

place on the Globe is situated - - 243

PROBLEM XXXIX. To find the breadths of the several

Climates between the Equator and the Polar Circles - 244

PROBLEM XL. To find that part of the equation of Time

which depends on the obliquity of the Ecliptic - - 245

PROBLEM XLI. To find the Sun's meridian altitude at any

time of the year at any given place - 247

PROBLEM XLII. When it is midnight at any place in the
Temperate or Torrid Zones, to find the Sun's altitude at
any place (on the same meridian) in the North Frigid
Zone, where the Sun does not descend below the horizon 249

PROBLEM XLII I. To find the Sun's amplitude at any place 250

PROBLEM XLIV. To find the Sun's azimuth and his alti-
tude at any place, the day and hour being given - 251

PROBLEM XL V. The latitude of the place, day of the month,
and the Sun's altitude being given, to find the Sun's azi-
muth and the hour of the day - . - - 253

PROBLEM XLVI. Given the latitude of the place, and the
day of the month, to find at what hour the Sun is due
east or west ----- 255

PROBLEM XLVII. Given the Sun's meridian altitude and
the day of the month, to find the latitude of the place - 25G

PROBLEM XLVIII. The length of the longest day at any
place, not within the Polar Circles, being given, to find
the latitude of that place
PROBLEM XLIX. The latitude of a place, and the day of

XX CONTENTS.

Page

the month being given, to find how much the sun's de-
clination must increase or decrease towards the elevated
Pole, to make the day an hour longer or shorter than the
given day ------ 259

PROBLEM L. To find the Sun's right ascension, oblique as-
cension, oblique descension, ascensional difference, and
time of rising and setting at any place - 261

PROBLEM LI. Given the day of the month, and the Sun's

amplitude, to find the latitude of the place of observation 262

PROBLEM LI I. Given two observed altitudes of the Sun,
the time elapsed between them, and the Sun's declination,
to find the latitude - - - - 263

PROBLEM LIII. The day and hour being given when a solar
eclipse will happen, to find where it will be visible - 265

PROBLEM LI V. The day and hour being given when a lunar
eclipse will happen, to find where it will be visible - 266

PROBLEM LV. To find the time of the year when the Sun

or Moon will be liable to be eclipsed - 270

PROBLEM LVI. To explain the phenomenon of the Har-
vest Moon --.-_. 27^2

PROBLEM LVII. The day and hour of an eclipse of any one
of the Satellites of Jupiter being given, to1 find upon the
Globe all those places where it will be visible - - 274

PROBLEM LVIII. To place the Terrestrial Globe in the
sunshine, so that it may represent the natural position of
the Earth - > 276

PROBLEM LIX. The latitude of a place being given, to find
the hour of the day at any time when the Sun shines - 278

PROBLEM LX. To find the Sun's altitude, ^by placing the

Globe in the sunshine - - - « 280

PROBLEM LXI. To find the Sun's declination, his place

i in the Ecliptic, and his Azimuth, by placing the globe in

the Sunshine - - _ _ _ 280

PROBLEM LXII. To draw a meridian line upon a horizontal
plane, and to determine the four cardinal points of the
horizon- 281

PROBLEM LXIII. To make a horizontal dial for any lati-

tude - - - 281

PROBLEM LXIV. To make a vertical dial facing the south
m north latitude - . _ _ „ _ 285

II. PROBLEMS PERFORMED BY THE CELESTIAL GLOBE,

f Q ° nd the rfght ascenslon and declin-
atton of the Sun, or a star - _ 288

PROBLEM LXVI. To find the latitude and longitude of a

290

CONTENTS. XXI

Page

PROBLEM LX VII. The right ascension and declination of
a Star, the Moon, a Planet, or of a Comet, being given,
to find its place on the Globe - - - - 291

PROBLEM LXVIII. The latitude and longitude of the
Moon, a Star, or a Planet given, to find its place on the
Globe ..... -292

PROBLEM LXIX. The day and hour, and the latitude of a
place being given, to find what Stars are rising, setting,
culminating, &c. - - ... 292

PROBLEM LXX. The latitude of a place, day of the month
and hour being given, to place the Globe in such a manner
as to represent the Heavens at that time, in order to find
out the relative situations and names of the Constellations
and remarkable Stars - - 294

PROBLEM LXXI. To find when any Star, or Planet, will

rise, come to the meridian, and set at any given place - 294

PROBLEM LXXII. To find the amplitude of any Star, its
oblique ascension and descension, and its diurnal arc, for
any given day - - . »;_J - 296

PROBLEM LXXIII. The latitude of a place given, to find
the time of the year at which any known Star rises or sets
acronically, that is, when it rises or sets at ^un-setting - 297

PROBLEM LXXIV. The ktitude of a place given, to find
the time of the year at which any known Star rises or set
cosmically, that is, when it rises or sets at sun-rising ' •'".] 298

PROBLEM LXXV. To find the time of the year when any

given star rises or sets heliacally ... 299

PROBLEM LXX VI. The latitude of a place and day of the
month being given, to find all those Stars that rise and set
acronically, cosmically, and heliacally - - 302

PROBLEM LXX VI I. To illustrate the precession of the

Equinoxes ..<•>.,:< - - 303

PROBLEM LXXVIII. To find the distances of the Stars
from each other in degrees - - - r •• r • • 305

PROBLEM LXXIX. To find what Stars lie in or near the
Moon's path, or what Stars the Moon can eclipse, or make
a near approach to 305

PROBLEM LXXX. Given the latitude of the place and the
day of the month, to find what Planets will be above the
horizon after sun-setting '".*;,, ~ " ~ 3^6

PROBLEM LXXXI. Given the latitude of the place, day of
the month, and hour of the night or morning, to find what
Planets will be visible at that hour - 307

PROBLEM LXXXII. The latitude of the place, and day of
the month given, to find how long Venus rises before the
Sun when she is a morning Star, and how long she-shines
after the Sun sets when she is an evening Star - - 30#

Xxii CONTENTS.

Page

PROBLEM LXXXIII. The latitude of a place, and day of
the month being given, to find the meridian altitude of any
Star or Planet - - 309

PROBLEM LXXXIV. To find all those places on the Earth

to which the Moon will be nearly vertical on any given day 311

PROBLEM LXXXV. Given the latitude of a place, day of
the month, and the altitude of a Star, to find the hour of
the night, and the Star's azimuth - - - 312

PROBLEM LXXXVI. Given the ktitude of a place, day
of the month, and hour of the day, to find the altitude of
any Star, and its azimuth - 314

PROBLEM LXXX VII. Given the latitude of a place, day of
the month, and azimuth of a Star, to find the hour of the
night, and the Star's altitude - - 315

PROBLEM LXXXVIII. Two Stars being given, the one on
the meridian, and the other on the east or west part of the
horizon, to find the latitude of the place - 316

PROBLEM LXXXIX. The latitude of the place, the day of
the month, and two Stars that have the same azimuth, being
given, to find the hour of the night - - 316

PROBLEM XC. The latitude of the place, the day of the
month, and two Stars that have the same altitude, being
given, to find the hour of the night - - 318

PROBLEM XCL The altitudes of two Stars having the same
azimuth, and that azimuth being given, to find the latitude
of the place ...... sis

PROBLEM XCII. The day of the month being given, and
the hour when any known Star rises or sets, to find the
ktitude of the place - - - - - 319

PROBLEM XCIII. To find on what day of the year any given

Star passes the meridian at any given hour - - 320

PROBLEM XCIV. The day of the month being given, to
find at what hour any given Star comes to the meridian - 321

PROBLEM XCV. Given the azimuth of a known Star, the
latitude, and the hour, to find the Star's altitude, and the
day of the month - 323

PROBLEM XCVI. The altitude of two Stars being given, to
find the latitude of the place - 324

PROBLEM XCVII. The meridian altitude of a known Star
being given, at any place in north latitude, to find the
latitude - _ 325

PROBLEM XCVIII. The latitude of a place, day of the
month, and hour of the day being given, to find the nona-
gesimal degree of the ecliptic, its altitude and azimuth,
and the medium cceli - 325

PROBLEM XCIX. The latitude of a place, day of the month,

CONTENTS.

and the hour, together with the altitude and azirautu of a

Star, being given, to find the Star
PROBLEM C. To find the time of the Moon's southing, or

coming to the meridian of any place, on any given day of

the month -

PROBLEM CI. The day of the month, latitude of the place,

and the time of high water at the full and change of the

moon, being given, to find the time of high water on the

given day -

PROBLEM C 1 1. To describe the apparent path of any Planet,

or of a Comet, amongst the fixed Stars, &c.

PROBLEMS WHICH MAY BE PERFORMED BY EITHER GLOBE.

PROBLEM XX.

XXV. -

XXVIII.

XXIX. -

XXX. -

XXXI. -

XXXII. -

XXXIII.

XXXIV.

XXXV. -

XXXVI.

XXXVII.

XXXVIII.

XXXIX.

XL.

XLI.

xxm
Page

327
328

329
333

Page
250
251
253
255
256
258
259
261
262
263
270
272
278
280
280

PART IV.

A promiscuous collection of examples exercising the pro-
blems on the Globes ----- 335 to 346

A collection of questions, with references to the pages
where the answers will be found ; designed as an assist-
ant to the tutor in the examination of the student - 347 to 361

INDEX TO THE TABLES.

I. A table of the climates . - - 18

II. Tables of the constellations, alphabetically arranged, with
the number of stars in each constellation, and the names of
the principal stars ; together with the right ascension and
declination of the middle of each constellation, for the

ready finding of them on the Globe - - 27, 28, 29

TIL A table of the velocity and pressure of the winds - 109

XXIV CONTENTS.

Page

IV. A table of the time of culminating of the zodiacal con-
stellations on the first day of every month, and the semi-
diurnal arc at London - - - - - 126 v

V. A table of the satellites of Jupiter - 163

VI. A table of the configurations of the satellites of Jupiter 165

VII. A table of the satellites of Saturn - 168

VIII. A table of the Epacts till the year 1900 - ISO

IX. A table showing the number of direction for finding

Easter Sunday - - . - • - - 181

X. A table for finding Easter till the year 1900 - 182

XI. A table for finding the moon's age, and the times of

new and full moon, till the year 1900 - 184

XII. Tabular view of the Planetary System - 186, 187

XIII. A table of the number of geographical and English
miles which make a degree in any given parallel of lati-
tude - - - 196

XIV. A table of the equation of time, dependent on the
obliquity of the ecliptic, for every degree of the sun's
longitude - - 246

XV. A table of all the visible eclipses which will happen

in the present century - - - • - - 267

XVI. A table of the hour arcs and angles for a horizontal

dial for the latitude of London - 284

XVII. A table of the hour arcs and angles for a vertical

dial for the latitude of London - - 287

XVIII. A table of the equation of time, to be placed on a
sun-dial . . 287

XIX. A table of the time of high water at new and full

moon, at the principal places in the British Islands - 332

XX. Etymological table of scientific words - - 362

SEVEN COPPER-PLATES to be placed at the End of tit* Book.

A NEW

TREATISE

ON THE

USE OF THE GLOBES, &c.

PART I.

DEFINITIONS AND INTRODUCTORY SUBJECTS.

CHAPTER I.

Explanation of the Lines on the Artificial Globes, including
Geographical and Astronomical Definitions ; with a few
Geographical Theorems.

1. THE TERRESTRIAL GLOBE is an artificial represent-
ation of the earth. On this globe the four great divisions
of the world, the different empires, kingdoms, and countries;
the chief cities, seas, rivers, &c. are truly represented,
according to their relative situation on the real globe of
the earth. The diurnal motion of this globe is from west
to east.

2. The CELESTIAL GLOBE is an artificial represent-
ation of the heavens, on which the stars are laid down in
their natural situations. The diurnal motion of this globe
is from east to west and represents the apparent diurnal
B

2 DEFINITIONS, &c. Part I.

motion of the sun, moon, and stars. In using this globe,
the student is supposed to be situated in the centre of it,
and viewing the stars in the concave surface.

3. The Axis OF THE EARTH [see Plate I. * Figures I.
and II.] is an imaginary line passing through its centre,
upon which it is supposed to turn, and about which all the
heavenly bodies appear to have a diurnal revolution. This
line is represented by the wire which passes from north to
south, through the middle of the artificial globe.

4. The POLES OF THE EARTH are the two extremities
of the axis, where it is supposed to cut the surface of the
earth, one of which is called the north, or arctic pole ; the
other the south, or antarctic pole. The celestial poles
are two imaginary points f in the heavens, exactly above
the terrestrial poles.

5. The BRAZEN MERIDIAN is the circle in which the
artificial globe turns, and is divided into 360 equal parts,
called degrees.^ In the upper semicircle of the brass
meridian these degrees are numbered from 0 to 90, from
the equator towards the poles, and are used for finding
the latitudes of places. On the lower semicircle of the
brass meridian they are numbered from 0 to 90 ; from the

* Figure I. represents the frame of the globe, with the horizon,
brass meridian, and axis : Figure II. the globe itself, with the lines on
its surface.

f The polar-star is a star of the second magnitude, near the north
pole, in the end of the tail of the Little Bear. Its right ascension,
for the beginning of the year 1840, was 1 h. 2m. 10-683 s.; and its
declination 88° 27' 21"-94 N. — Nautical Almanac for 1840.

| Every circle is supposed to be divided into 360 equal parts called
degrees, each degree into 60 equal parts called minutes, each minute
into 60 equal parts called seconds, &c. ; a degree is therefore only a
relative idea, and not an absolute quantity, except when applied to a
great circle of the earth, as to the equator or to a meridian, in which
cases it is 60 geographical miles, or 69 '1 English miles. A degree of
a great circle in the heavens is a space nearly equal to twice the appa-
rent diameter of the sun ; or to twice that of the moon when consider-
ably elevated above the horizon.

Degrees are marked with a small cipher, minutes with one dash,
seconds with two, thirds with three, &c. Thus 25 14' 22" 35'" are
read 25 degrees, 14 minutes, 22 seconds, 35 thirds.

Chap. I. DEFINITIONS, &c. 3

poles towards the equator, and are used in the elevation
of the poles.

6. GREAT CIRCLES divide the globe into two equal
parts, as the equator, ecliptic, and the colures.

7. SMALL CIRCLES divide the globe into two unequal
parts, as the tropics, polar circles, parallels of latitude,
&c.

8. MERIDIANS, or Lines of Longitude, are semicircles,
extending from the north to the south pole, and cutting
the equator at right angles. Every place upon the globe
is supposed to have a meridian passing through it, though
there be only 24 drawn upon the terrestrial globe ; the
deficiency is supplied by the brass meridian. When the
sun comes to the meridian of any place (not within the
polar circles), it is noon or mid-day at that place.

9. The FIRST MERIDIAN is that from which geogra-
phers begin to count the longitudes of places. In
English maps and globes the first meridian is a semi-
circle supposed to pass through the Royal Observatory at
Greenwich.

10. The EQUATOR is a great circle of the earth, equi-
distant from the poles : it divides the globe into two
hemispheres, northern and southern. The latitudes of
places are counted from the equator, northward and
southward, and the longitudes of places are reckoned
upon it eastward and westward.

The equator, when referred to the heavens, is called
the equinoctial, because when the sun appears in it, the
days and nights are equal all over the world, viz. 12 hours
each. The declinations of the sun, stars, and planets, are
counted from the equinoctial northward and southward,
and their right ascensions are reckoned upon it eastward
round the celestial globe from 0 to 360 degrees.

11. The ECLIPTIC is a great circle in which the sun
makes his apparent annual* progress among the fixed

* The sun's apparent diurnal path is either in the equinoctial, or in
lines nearly parallel to it ; and his apparent annual path may be traced
in the heavens, by observing what particular constellation in the zodiac
is on the meridian at midnight ; the opposite constellation will show,
very nearly, the sun's place at noon on the same day.
B 2

DEFINITIONS, &C.

Parti.

stars, and is therefore sometimes called the via soils or
sun's path ; but more properly it is the track which the
earth would appear to describe if viewed from the centre
of the sun, and is hence denominated the heliocentric
circle of the earth. It is named the ecliptic, because
eclipses can only happen when the moon appears to be in
or very near to this circle. The ecliptic cuts the equinoc-
tial at an angle of 23° 28' ; the points of intersection are
called the equinoctial points.

12. The ZODIAC, on the celestial globe, is a space
which extends about nine degrees on each side of the
ecliptic, like a belt or girdle, within which the motions of
all the planets* are performed.

13. SIGNS OF THE ZODIAC. The ecliptic and zodiac
are divided into 12 equal parts, called signs, each contain-
ing 30 degrees. The sun makes his apparent annual pro-
gress through the ecliptic at the rate of nearly a degree
in a day. The names of the signs, and the days on which
the sun enters them, are as follow : —

SPRING SIGNS.
V Aries, the Ram, 21st of

March.
« Taurus, the Bull, 19th

of April,
n Gemini, the Twins, 20th

of May.

SUMMER SIGNS.
23 Cancer, the Crab, 21st

of June.
SI Leo, the Lion, 22d of

July.
fl£ Virgo, the Virgin, 22d

of August.

These are called northern signs, being north of the
equinoctial.

AUTUMNAL SIGNS.

Libra, the Balance, 23d
of September.

Scorpio, the Scorpion,
23d of October.

Sagittarius, the Archer,
22d of November

WINTER SIGNS.

Ttf Capricornus, the Goat,
21st December.

£Z Aquarius, the Water-
bearer, 20th January.

X Pisces, the Fishes, 19th
February.

« Except three of the newly discovered minor primary planets, viz.
Ceres, Pallas, and Juno.

Chap. I. DEFINITIONS, &c. 5

These are called southern signs.

The spring and autumnal signs are called ascending
signs ; because when the sun is in any of these, his de-
clination is increasing. The summer and winter signs
are called descending signs, because when the sun is in
any of these, his declination is decreasing.

14. The COLURES are two great circles passing through
the poles of the world ; one of them passes through the
equinoctial points, Aries * and Libra; the other through
the solstitial points, Cancer and Capricorn ; hence they
are called the equinoctial and solstitial colures. They
divide the ecliptic into four equal parts, and mark the
four seasons of the year.

15. DECLINATION of the sun, of a star, or planet, is its
distance from the equinoctial, northward or southward.
When the sun is in the equinoctial he has no declination,
and enlightens half the globe from pole to pole. As he
Increases in north declination he gradually shines farther
over the north pole, and leaves the south pole in dark-
ness : in a similar manner, when he has south declination,
he shines over the south pole, and leaves the north pole
in darkness. The greatest declination the sun can have
is 23° 28' ; the greatest declination a star can have is 90°,
and that of a planet 30° 28' f north or south.

16. The TROPICS are two small circles, parallel to the
equator (or equinoctial), at the distance of 23° 28' from it ;
the northern is called the Tropic of Cancer, the southern
the Tropic of Capricorn. The tropics are the limits of
the torrid zone, northward and southward.

17. The POLAR CIRCLES are two small circles, parallel
to the equator (or equinoctial), at the distance of 66° 32"
from it, and 23° 28' from the poles. The northern is
called the arctic, the southern the antarctic circle.

* In the time of Hipparchus the equinoctial colure is supposed to
have passed through the middle of the constellation Aries. Hipparchus
was a native of Nicsea, a town of Bithynia, in Asia Minor, about 75
miles S. E. of Constantinople, now called Isnic ; he made his observ-
ations between 160 and 135 years before Christ.

T Except the minor primary planets, CereS) Juno, and Pallas, whose
orbits are so much inclined to the ecliptic as considerably to exceed
the limits of the zodiac.

B 3

6 DEFINITIONS, &c. Part I.

18. PARALLELS OF LATITUDE are small circles drawn
through every ten degrees of latitude, on the terrestrial
globe, parallel to the equator. Every place on the globe
is supposed to have a parallel of latitude drawn through
it, though there are generally only sixteen parallels of lati-
tude drawn on the terrestrial globe.

19. The HOUR CIRCLE on the artificial globes is a
small circle of brass, with an index or pointer fixed to the
north pole : it is divided into 24-* equal parts, correspond-
ing to the hours of the day, and these are again sub-
divided into halves and quarters. The hour circle, when
placed under the brass meridian, is movable round the
axis of the globe, and the brass meridian, in this case,
answers the purpose of an index.

20. The HORIZON is a great circle which separates the
visible half of the heavens from the invisible ; the earth
being considered as a point in the centre of the sphere of
the fixed stars. Horizon, when applied to the earth, is
either sensible or rational.

21. The SENSIBLE, or visible horizon, is the circle
which bounds our view, where the sky appears to touch
the earth or sea. t

22. The RATIONAL, or true horizon, is an imaginary
plane, passing through the centre of the earth parallel to

* Some globes have two rows of figures ou the index, others but
one. On Bardiris New British Globes there is an hour circle at each
pole, numbered with two rows of figures. On Adams's common
globes there is but one index ; and on his improved globes the hours
are counted by a brass wire with two indexes standing over the
equator. The form of the hour circle is, however, a matter of little
consequence (provided it be placed under the brass meridian), as the
equator will answer every purpose to which a circle of this kind can be
applied.

t The sensible horizon extends only a few miles ; for example, if
the eye of a spectator supposed out at sea or standing on an extensive
plane be elevated 6 feet above the surface of the sea or the plane on
which he stands, the utmost extent of his view upon that surface or
plane would be about three miles. Thus, if h be the height of the eye
above the surface of the sea, and d the diameter of the earth in feet, then
A/(d + A) x h, will show the distance which a person will be able to see,
straight forward. Keith's Trigonometry, Seventh Edition. Examule
XLV. page 82.

Chap. I. DEFINITIONS, &c. 7

the sensible horizon. It determines the rising and setting
of the sun, stars, and planets.

23. The WOODEN HORIZON, circumscribing the arti-
ficial globe, represents the rational horizon on the real
globe. This horizon is divided into several concentric
circles, which on Bardiris * New British Globes are ar-
ranged in the following order: —

The First is marked amplitude, and is numbered from
the east towards the north and south, from 0 to 90 de-
grees, and from the west towards the north and south in
the same manner.

The Second is marked azimuth, and is numbered from
the north point of the horizon towards the east and west,
from 0 to 90 degrees : and from the south point of the
horizon towards the east and west in the same manner.

The Third contains the thirty-two points of the com-
pass, divided into half and quarter points. The degrees
in each point are to be found in the azimuth circle.

The Fourth contains the twelve signs of the zodiac, with
the figure and character of each sign.

The Fifth contains the degrees of the signs, each sign
comprehending 30 degrees.

The Sixth contains the days of the month answering to
each degree of the sun's place in the ecliptic.

The Seventh contains the equation of time, or difference
of time shown by a well-regulated clock and a correct sun-
dial. When the clock ought to be faster than the dial,
the number of minutes, expressing the difference, is fol-
lowed by the sign -f- ; when the clock or watch ought to
be slower, the number of minutes in the difference is fol-
lowed by the sign — .

The Eighth contains the twelve calendar months.

24-. The CARDINAL POINTS of the horizon are east,
west, north, and south.

* GARY'S Globes have a different division of the wooden horizon.
The first circle, or that nearest to the globe, is numbered from the east
and west towards the north and south, from 0 to 90°. The second
contains the thirty-two points of the compass. The third the signs of
the zodiac. The fourth the degrees of the signs. The fifth the days
of the months. The sixth the names of the months. The wooden
horizon of ADAMS'S Globes is divided in the same manner.
B 4<

8 DEFINITIONS, &c. Part I.

25. The CARDINAL POINTS in the heavens are the ze-
nith; the nadir, and the points where the sun rises and sets.

26. The CARDINAL POINTS of the ecliptic are the
equinoctial and solstitial points, which mark out the four
seasons of the year ; and the Cardinal Signs are V Aries,
S3 Cancer, ;£= Libra, and Ttf Capricorn.

27. The ZENITH is a point in the heavens exactly over
our heads, and is the elevated pole of our horizon.

28. The NADIR is a point in the heavens exactly under
our feet, being the depressed pole of our horizon, and
the zenith, or elevated pole, of the horizon of our antipodes.

29. The POLE of any circle is a point on the surface
of the globe, 90 degrees distant from every part of that
circle of which it is the pole. Thus the poles of the earth
are 90 degrees from every part of the equator ; the poles
of the ecliptic (on the celestial globe) are 90 degrees
from every part of the ecliptic, and 23° 28' from the poles
of the equinoctial, consequently they are situated in the
arctic and antarctic circles. Every circle on the globe,
whether real or imaginary, has two poles diametrically
opposite to each other.

SO. The EQUINOCTIAL POINTS are Aries and Libra,
where the ecliptic cuts the equinoctial. The point Aries
is called the vernal equinox, and the point Libra the au-
tumnal equinox. When the sun is in either of these
points, the days and nights on every part of the globe are
equal to each other.

31. The SOLSTITIAL POINTS are Cancer and Capricorn.
When the sun is in, or near, these points, the variation in
his greatest or meridian altitude is scarcely perceptible
for several days ; because the ecliptic near these points is
almost parallel to the equinoctial, and therefore the sun
has nearly the same declination for several days. — When
the sun enters Cancer, it is the longest day to all the
inhabitants on the north side of the equator, and the
shortest day to those on the south side. When the sun
enters Capricorn it is the shortest day to those who live
in north latitude, and the longest day to those who live
in south latitude.

32. A HEMISPHERE is half the surface of the globe ;
every great circle divides the globe into two hemispheres

C/Utp. I. DEFINITIONS, &O, 9

The horizon divides the upper from the lower hemisphere
in the heavens ; the equator separates the northern from
the southern on the earth ; and the brass meridian, stand-
ing, over anyplace on the terrestrial globe, divides the
eastern from the western hemisphere.

33. The MARINER'S COMPASS * is a representation of
the horizon, and is used by seamen to direct and ascer-
tain the course of their ships. It consists of a circular
brass box, which contains a paper card, divided into 32
equal parts, and fixed on a magnetical needle that always
turns towards the north. Each point of the compass
contains 11° 15' or 11^ degrees, being the 32d part of
360 degrees.

84. The VARIATION OF THE COMPASS is the deviation
of its points from the corresponding points in the heavens.
When the north point of the compass is to the east of the
true north point of the horizon, the variation is east : if
it be to the west, the variation is west.

* Though the attractive power of the magnet, or loadstone, was
known to the Greeks at least as early as the time of Plato arid Aristotle,
yet the directive power of it, or that property whereby it disposes bars
of iron or steel touched with it to lie along the plane of the meridian
of any place, so as to point nearly due North and South, was certainly
entirely unknown to them : neither is it satisfactorily proved by whom
this property was discovered. By some it is ascribed to Paul the
Venetian, who, it is said, first brought into use (about the year 1260)
what is now called the Mariner's Compass. By others this instrument
is said to have been invented by John Goia, a Neapolitan, in the year
1300; who is also spoken of as the first person who applied it to navi-
gating ships in the Mediterranean.

The Variation of the needle, or its declination from the true north
and south points, is a much later discovery, and is generally ascribed
to Sebastian Cabot, a Venetian, or as some will have it, the son of a
Genoese merchant, who resided at Bristol, where Sebastian was born.
This discovery was made about the year 1497, previous to which any
deviation of the direction of the needle from the plane of the meridian
was supposed to arise from some defect in the construction of the par-
ticular instrument in which it was observed. The variation of the
needle was, as might naturally be expected, long considered constant,
or to be invariably the same at the same place ; nor was the variation,
to which what is called the variation of the needle is itself subject, fully
ascertained till about the year 1625, when, according to Dr. Wallis
(Philos. Trans. Nos. 276 — 278.), it was first discovered by Mr. Gil-
librand, one of the professors at Gresham College. — ED.
B 5

DEFINITIONS, &C.

Part I.

At present, in England, the needle points about 23J
degrees to the westward of the north.
At LONDON in

,llc

> 15' E.

1790,

10 E.

1794,

0 E.

1796,

5 E.

1800,

1804,

35 W.

1806,

sow.

1820,

0 W.

1823,

22 W.

1831,

40 W.

1842,

10W.

23
23
24
24
24
24
*24
24
24
23

39 W.
54 W.

ow.

2 W.
8 W.
8 W.

34 W.

low.

0 W.
11 W.

1612,
1622,
1634,
1657,
1666,
1683,
1700,
1722,
1747,
1780,

The compass is used for setting the artificial globe north and south ;
but care must he taken to make a proper allowance for the variation.

35. LATITUDE OF A PLACE, on the terrestrial globe,
is its distance from the equator in degrees, minutes, or
geographical miles, &c. and is reckoned on the brass me-
ridian, from the equator towards the north or south pole.

36. LATITUDE OF A STAR OR PLANET, on the celes-
tial globe, is its distance from the ecliptic, northward or
southward, counted towards the pole of the ecliptic, on
the quadrant of altitude. The greatest latitude a star
can have is 90 degrees, and the greatest latitude of a
planet is nearly 8 degrees, f The sun being always in the
ecliptic, has no latitude.

37. The QUADRANT OF ALTITUDE is a thin flexible
piece of brass divided upwards from 0 to 90 degrees,
and downwards from 0 to 18 degrees, and when used is
generally screwed to the brass meridian. The upper divi-
sions are used to determine the distances of places on the
earth, the distances of the celestial bodies, their altitudes,
&c., and the lower divisions are applied to finding the
beginning, end, and duration of twilight.

38. LONGITUDE O,F A PLACE, on the terrestrial globe,
is the distance of the meridian of that place from the first
meridian, reckoned in degrees and parts of a degree on the

* The needle had made an angle more and more westward, till
ahout 1820, when it arrived at 24° 34' W. ; since which time its mo-
tion has been retrograde, being now about 23° 107 W.

f The newly- discovered planets, or Asteroids, Ceres and Pallas, &c
do not appear to be confined within this limit.

. DEFINITIONS, &C. 11

equator. Longitude is either eastward or westward,
according as the place is eastward or westward of the
first meridian. The greatest longitude that a place can
have is 180 degrees, or half the circumference of the
globe.

39. LONGITUDE OF A STAR, or PLANET, is reckoned
on the ecliptic from the point Aries, eastward, round the
celestial globe. The longitude of the sun is what is called
the sun's place on the terrestrial globe.

40. ALMACANTARS, or parallels of altitude, are imagi-
nary circles parallel to the horizon, and serve to shew the
height of the sun, moon; or stars. These circles are not
drawn on the globe, but they may be described for any
latitude by the quadrant of altitude.

41. PARALLELS OF CELESTIAL LATITUDE are small
circles drawn on the celestial globe parallel to the
ecliptic.

42. PARALLELS OF DECLINATION are small circles
parallel to the equinoctial on the celestial globe, and
are similar to the parallels of latitude on the terrestrial
globe.

43. AZIMUTH, or VERTICAL CIRCLES, are imaginary
great circles passing through the zenith and the nadir,
cutting the horizon at right angles. The altitudes of the
heavenly bodies are measured on tjiese circles, which
circles may be represented by screwing the quadrant of
altitude on the zenith of any place, and making the other
end move along the wooden horizon of the globe.

44. The PRIME VERTICAL is that azimuth circle which
passes through the east and west points of the horizon,
and is always at right angles to the brass meridian, which
may be considered as another vertical circle passing
through the north and south points of the horizon.

45. The ALTITUDE of any object in the heavens is an
arc of a vertical circle, contained between the centre of
the object and the horizon. When the object is upon the
meridian, this arc is called the meridian altitude.

46. The ZENITH DISTANCE of any celestial object is
the arc of a vertical circle, contained between the centre
of that object and the zenith ; or it is what the altitude of
the object wants of 90 degrees. When the object is on

B 6

12 DEFINITIONS, &c. Part I.

the meridian, this arc is called the meridian zenith
distance.

47. The POLAR DISTANCE of any celestial object is an
arc of a meridian, contained between the centre of that
object and the pole of the equinoctial.

4*8. The AMPLITUDE of any object in the heavens is
an arc of the horizon, contained between the centre of
the object when rising, or setting, and the east or west
points of the horizon. Or, it is the distance which the
sun or a star rises from the east, and sets from the west,
and is used to find the variation of the compass at sea.
When the sun has north declination, it rises to the north
of the east, and sets to the north of the west ; and when
it has south decimation, it rises to the south of the east,
and sets to the south of the west. At the time of the
equinoxes, when the sun has no declination, viz. on the
21st of March, and on the 23d of September, it rises ex-
actly in the east, and sets exactly in the west.

49. The AZIMUTH of any object in the heavens is an
arc of the horizon, contained between a vertical circle
passing through the object, arid the north or south points
of the horizon. The azimuth of the sun, at any parti-
cular hour, is used at sea for finding the variation of the
compass.

50. HOUR CIRCLES, or HORARY CIRCLES, are the same
as the meridians. They are drawn through every 15 de-
grees* of the equator, each answering to an hour —
consequently every degree of longitude answers to four
minutes of time, every half degree to two minutes, and
every quarter of a degree to one minute.

On the globes these circles are supplied by the brass
meridian, the hour circle and its index.

51. The Six O'CLOCK HOUR LINE. As the meridian
of any place, with respect to the sun, is called the 12
o'clock hour circle ; so that great circle passing through
the poles, which is 90 degrees distant from it on the
equator, is called by astronomers the six o'clock hour

* On Card's large Globes the meridians are drawn through every
10 degrees, as on a Map.

I. DEFINITIONS, &C. 13

circle, or the six o'clock hour line: The sun and stars
are on the eastern half of this circle 6 hours before they
come to the meridian ; and on the western half six hours
after they have passed the meridian.

52. CULMINATING POINT of a star or planet is that
point of its orbit which, on any given day, is the most
elevated. Hence a star or planet is said to culminate
when it comes to the meridian of any place ; for then its
altitude at that place is the greatest.

53. APPARENT NOON is the time when the sun comes
to the meridian ; viz. 12 o'clock, as shewn by a correct
sun-dial.

54. TRUE or MEAN NOON, 12 o'clock, as shewn by a
well-regulated clock, adjusted to go 24- hours in a mean
solar day.

55. The EQUATION OF TIME at noon is the interval
between the true and apparent noon, viz. it is the differ-
ence of time shewn by a well-regulated clock and a cor-
rect sun-dial.

56. A TRUE SOLAR DAY is the time from the sun's
leaving the meridian of any place, on any day, till it re-
turns to the same meridian on the next day ; viz. it is the
time elapsed from 12 o'clock at noon, on any day, to 12
o'clock at noon on the next day, as shewn by a correct
sun-dial. A true solar day is subject to a continual va-
riation, arising from the obliquity of the ecliptic, and the
unequal motion of the earth in its orbit ; the duration
thereof sometimes exceeds, at others falls short of 24
hours, and the variation is the greatest about the first of
November, when the true solar day is 16' 17" less than
24 hours, as shewn by a well-regulated clock.

57. A MEAN SOLAR DAY is measured by equal mo-
tion, as by a clock or time-piece, and consists of 24 hours.
There are in the course of a year as many mean solar
days as there are true solar days, the clock being as much
faster than the sun-dial on some days of the year, as the
sun-dial is faster than the clock on others. Thus the
clock is faster than the sun-dial from the 24th of Decem-
ber to the 15th of April, and from the 16th of June to
the 31st of August: but from the 15th of April to the
16th of June, and from the 31st of August to the 24th

14 DEFINITIONS, &c. Parti.

of December, the sun-dial is faster than the clock. When
the clock is faster than the sun-dial, the true solar day
exceeds 24 hours ; and when the sun-dial is faster than
the clock, the true solar day is less than 24 hours ; but
when the clock and the sun-dial agree, viz. about the 15th
of April, 16th of June, 31st of August, and 24th of De-
cember, the true solar day is exactly 24 hours.

58. The ASTRONOMICAL DAY is reckoned from noon
to noon, and consists of 24 hours. This is called a natural
day, being of the same length in all latitudes.

59. The ARTIFICIAL DAY is the time elapsed between
the sun's rising and setting, and is variable according to
the different latitudes of places.

60. The CIVIL DAY, like the astronomical or natural
day, consists of 24 hours, but begins differently in differ-
ent nations. The ancient Babylonians, Persians, Syrians,
and most of the eastern nations, began their day at sun-
rising. The ancient Athenians, the Jews, &c. began their
day at sun-setting, which custom is followed by the mo-
dern Austrians, Bohemians, Silesians, Italians, Chinese,
&c. The Arabians begin their day at noon, like the
modern astronomers. The ancient Egyptians, Romans,
&c. began their day at midnight, and this method is fol-
lowed by the English, French, Germans, Dutch, Spanish,
and Portuguese.

61. A SIDEREAL DAY is the interval of time from the
passage of any fixed star over the meridian, till it returns
to it again: or it is the time which the earth takes to
revolve once round its axis, and consists of 23 hours, 56
minutes, 4'09 seconds of mean solar time.

In elementary books of astronomy and the globes, the learner is
generally told that the earth turns on its axis from west to east in 24
hours ; but the truth is, that it turns on its axis in 23 hours, 56 mi-
nutes, 4-09 sees., making about 366 revolutions in 365 days, or a
year. The natural day would always consist of 23 hours, 56 minutes.
4-09 sees., instead of 24 hours, if the earth had no other motion than
that on its axis ; but while the earth has revolved eastward once
round its axis, it has advanced nearly one degree * eastward in its

» The earth goes round the sun in 365J days nearly ; and the
ecliptic, which is the earth's path round the sun, consists of 360

Chap. I. DEFINITIONS, £c. 15

orbit. To illustrate this, suppose the sun to be upon any par-
ticular meridian at 12 o'clock on any day ; in 23 hours, 56 minutes,
4 '09 sees., afterwards the earth will have performed one entire
revolution ; but it will at the same time have advanced nearly one
degree eastward in its orbit, and consequently that meridian which
was opposite to the sun the day before, will be now one degree
westward . of it ; therefore the earth must perform something more
than one revolution before the sun appears again on the same meri-
dian ; so that the time from the sun's being on the meridian on
any day, to its appearance on the same meridian the next day, is
24 hours.

62. A SOLAR YEAR, or tropical year, is the time the
sun takes in passing through the ecliptic, from the tropic,
or equinox, till it returns to it again : and consists of 365
days, 5 hours, 4-8 minutes, 49 seconds.

63. A SIDEREAL YEAR is the time which the sun
takes in passing from any fixed star, till he returns to it
again, and consists of 365 days, 6 hours, 9 minutes, 12
seconds ; the sidereal year is therefore 20 minutes, 23 se-
conds longer than the tropical year, and the sun returns
to the equinox every year before he returns to the same
point of the heavens ; consequently the equinoctial points
have a retrograde motion.

64. THE PRECESSION OF THE EQUINOXES (or more
properly the recession of the equinoxes (is a slow motion
which the equinoctial points have from east to west, con-
trary to the order of the signs, which is from west to east.

This motion, from the best observations, is about 50*1*
seconds in a year, so that it would require 25,868 years -j-
for the equinoctial points to perform an entire revolution
westward round the globe.

In the time of Hipparchus and the oldest astronomers, the equinoc-
tial points were fixed in Aries and Libra : but the signs which were

degrees ; hence by the rule of three, 365\ D I 360 deg. ; ; 1 D '.
59' 8".3, the daily mean motion of the earth in its orbit, or the ap-
parent mean motion of the sun in a day. Hence a clock or chrono-
meter, the index of which performs an exact circuit whilst the earth
(or the meridian of an observer) moves over 360° 59' 8". 3, is said to
be adjusted to mean solar time.

* Jn Woodhouse's Astronomy, the mean annual precession is stated
to be 50". 34, and in the new French Solar Tables 50". 103.

•J* For the circumference of the equator is 360 degrees, and 50".l '.
1 year : : 360 : 25,868 years.

15 DEFINITIONS, &c. Part I.

then in conjunction with the sun, when he was in the equinox, are
now a whole sign, or SO degrees eastward of it ; so that Aries is now
in Taurus, Taurus in Gemini, &c. as may be seen on the celestial
o-lobe. Hence also the stars, which rose and set at any particular
season of the year in the time of Hesiod*, Eudoxusf, Pliny}, £c. do
not answer to the description given by those writers.

65. POSITIONS OF THE SPHERE are three: right, pa-
rallel, and oblique.

66. A RIGHT SPHERE is that position of the earth
where the equinoctial passes through the zenith and the
nadir, the poles being in the rational horizon. The inha-
bitants who have this position of the sphere live at the
equator : it is called a right sphere, because the parallels
of latitude cut the horizon at right angles. In a right
sphere the parallels of latitude are divided into two equal
parts by the horizon, and the days and nights are of equal
length.

67. A PARALLEL SPHERE is that position the earth has
when the rational horizon coincides with the equator, the
poles being in the zenith and nadir. The inhabitants who
have this position of the sphere (if there be any such
inhabitants) live at the poles; it is called a parallel
sphere, because all the parallels of latitude are parallel to
the horizon. In a parallel sphere the sun appears above
the horizon for six months together, and he is below the
horizon for the same length of time.

* HESIOD was a celebrated Grecian poet, born at Ascra in Boeotia,
supposed to have flourished in the time of Homer ; he was the first who
wrote a poem on Agriculture, entitled The Works and the Days, in
which he introduces the rising and setting of particular stars, &c.
Several editions of his work are now extant.

f EUDOXUS was a great geometrician and astronomer, from whom
Euclid, the geometrician, is said to have borrowed great part of his
elements of geometry. Eudoxus was born at Cnidus, a town of Caria,
in Asia Minor ; he flourished about 370 years before Christ.

t PUNY, generally called Pliny the Elder, was born at Verona, in
Italy ; he composed a work on natural history in 37 books ; it treats
of the stars, the heavens, wind, rain, hail, minerals, trees, flowers,
plants, birds, fishes, and beasts ; besides a geographical description of
every place on the globe, &c. &c. Pliny perished by an eruption of
Vesuvius, in the 79th year of Christ, from too eager a curiosity in ob-
serving the phenomenon.

Chap. I. DEFINITIONS, &C. 1?

68. An OBLIQUE SPHERE is that position the earth
has when the rational horizon cuts the equator obliquely,
and hence it derives its name. All inhabitants on the
face of the earth (except those who live exactly at the
poles or at the equator) have this position of the sphere.
The days and nights are of unequal lengths, the parallels
of latitude being divided into unequal parts by the rational
horizon.

69. CLIMATE is a part of the surface of the earth con-
tained between two small circles parallel to the equator,
and of such a breadth, that the longest day in the parallel
nearest the pole, exceeds the longest day in the parallel
of latitude nearest the equator, by half an hour, in the
torrid and temperate zones, or by a month in the frigid
zones ; so that there are 24- climates between the equator
and each polar circle, and six climates between each polar
circle and its pole.

From the above definition, it appears that all places situated on the
same parallel of latitude are in the same climate ; but we must not
infer from thence that they have the same atmospherical temperature ;
large tracts of uncultivated lands, sandy deserts, elevated situations,
woods, morasses, lakes, &c. have a considerable effect on the atmo-
sphere. For instance, in Canada, in about the latitude of Paris
and the south of England, the cold is so excessive, that the greatest
rivers are frozen over from December to April, and the snow com-
monly lies from four to six feet deep. The Andes mountains,
though part of them is situated in the torrid zone, are at the summit
covered with snow, which cools the air in the adjacent country. The
heat on the western coast of Africa, after the wind has passed over the
sandy desert, is almost suffocating ; whilst the same wind having
passed over the Atlantic Ocean, is cool and pleasant to the inhabitants
of the Caribbean Islands.

DEFINITIONS, &C.

Part I.

I. CLIMATES between the EQUATOR and the POLAR CIRCLES, j

Climate.

Ends
inLati-
tude.

Where
the
longest
Day is.

Breadths
of the
Climates.

Climate.

Ends
inLati-
tude. *

Where '
the
longest
Day is.

Breadths
of the
Climates.

D. M.

H. M.

D. M.

H. M.

D. M.

8 34

12 30

8 34

XIII

59 59

18 30

1 32

1G 44

13 —

8 10

XIV

61 18

19 —

1 19

III

24 12

13 30

7 28

62 26

19 30

1 8

1 IV

30 48

14 —

6 36

XVI

63 22

20 —

— 56

36 31

14 30

5 43

XVII 64 10

20 30

— 48

41 24

15 —

4 53

XVIII

64 50

21 __ 40

VII

45 32

15 30

4 8

XIX

65 22

21 30

— 32

VIII

49 2

16 —

3 30

65 48

22 —

— 26

51 59

16 30

2 57

XXI

66 5

22 30

— 17

X 54 30

17 —

2 31

XXII

66 21

23 —

— 16

XI 56 38

17 30

2 8

XXIII ',66 2923 30

— 8

XII '58 27

18 —

1 49

XXIV

66 32

24 —

— 3

II. CLIMATES between the POLAR CIRCLES and the POLES.

Ends

Where

Breadths

Ends

Where

Breadths

Climate.

inLati-
tude.

the
longest
Day is.

of the
Climate*

Climate.

inLati-
tude.

the
longest
Day is.

of the
Climates.'

D. M.

Da. M.

D. M.

Da.M.

D. M.

XXV

G7 18 30 or 1 — 46

XXVIII

77 40

120or4

4 35

XXVI

69 33 60 — 2

2 15

XXIX

82 59

150—5

5 19

XXVII 73 590 — 3

3 32

XXX

90 —

180—6

7 1

The preceding tables may be constructed by the globes, as will be
shewn in the problems, but not with that exactness given above.
Tables of this kind are generally copied from one author into another,
without any explanation of the principles on which they are founded.

Construction of thejirst Table.

In plate IV. figure IV. HO represents the horizon, MQ. the equator,
25 c SB a parallel of the sun's greatest declination, NO the elevation of
the pole or latitude of the place ; the angle cab measured by the
arc QO, the complement of the latitude ; a b is the ascensional dif-
ference, or the time the sun rises before six o'clock, and b c the sun's
declination. Hence, by Baron Napier's rules, (see A'eit/i's Spherical
trigonometry,) rad. x sine a b = cotangent a* (or tangent NO]
x tangent be.

Chap. I.

DEFINITIONS, &C.

viz. Tangent of the sun's greatest declination 23° 28',
Is to radius, sine of 90 degrees ;
As sine of the sun's ascensional difference,

Is to tangent of latitude. A general rule.

At the end of the first climate the sun rises \ before 6 ; and in
every climate, if you take half the length of the longest day, and de-
duct 6 hours therefrom, the remainder turned into degrees will give
the ascensional difference. Hence the ascensional difference, for the
first climate, is fifteen minutes of time, equal to 3° 45' ; for the second
climate 30 minutes = 7° 30'; for the third climate 45 minutes =
11° 15' ; for the fourth climate 1 hour = 15°, &c.

Tangent of 23° 28' 9.63761

Is to radius, sine of 90° .10.00000
As sine of 3° 45' 8.81560

Tangent of 23° 28' 9.63761

Is to radius, sine of 90° .10.00000
As sine of 7° 30' 9.11570

Is to tang. lat. 8° 34'.... 9.17799 Is to tang. lat. 16° 44'. 9.47809

Construction of the second Table.

The longest day is the 21st of June, when the sun's declination is
23° 28' north. Count half the length of the day from the 21st June,
forward and backward ; find the sun's declination answering to those
two days in the nautical almanac, or in a table of the sun's declin-
ation ; add the two declinations together, and divide their sum by 2,
subtract the quotient from 90 degrees, and the remainder is the lati-
tude. As the sun's declination is variable, it ought to be taken out
of the almanac, or tables, for leap-year and the three following years,
a mean of these declinations, used as above, will give the latitude as
correctly as the nature of the problem admits of, and in this manner the
second table was constructed. — RICCIOI.I, (an Italian astronomer and
mathematician, born at Ferrara, in the Pope's dominions, 1598,) in
his Astronomic Reformatce, published in 1665, makes an allowance for
the refraction of the atmosphere in a table of climates. He con-
siders the increase of days to be by half hours, from 12 to 16 hours ;
by hours from 1 6 to 20 hours ; by 2 hours, from 20 to 24 hours ; and
by months in the frigid zones, making the number of the days of each
month in the north frigid zone something more than those in the south;
but as the refraction of the atmosphere is so extremely variable, that
scarcely any two mathematicians agree with respect to the quantity, it
is evident that a table of climates, calculated with such an uncertain
allowance, can be of no material advantage.

70. A ZONE is a portion of the surface of the earth
contained between two small circles parallel to the equa-
tor, and is similar to the term climate, for pointing out
the situations of places on the earth, but less exact ; as
there are only jive zones, which have been distinguished
by particular names ; whereas there are GO climates.

20 DEFINITIONS, &c. Part 1.

71. The TORRID ZONE extends from the tropic of
Cancer to the tropic of Capricorn, and is 46° 56' broad.
This zone was thought by the ancients to be uninhabited,
because it is continually exposed to the direct rays of the
sun ; and such parts of the torrid zone as were known to
them were sandy deserts, as the middle of Africa, Arabia,
&c. ; and these sandy deserts extend beyond the left
bank of the Indus, toward Agimere.

72. The Two TEMPERATE ZONES. The north tem-
perate zone extends from the tropic of Cancer to the
arctic circle ; and the south temperate zone from the
tropic of Capricorn to the antarctic circle. These zones
are each 43° 4' broad, and were called temperate by the
ancients, because meeting the sun's rays obliquely, they
enjoy a moderate degree of heat.

73. The Two FRIGID ZONES. The north frigid zone,
or rather segment of the sphere, is bounded by the arctic
circle. The north pole, which is 23° 28' from the arctic
circle, is situated in the centre of this zone. The south
frigid zone is bounded by the antarctic circle, distant
23° 28' from the south pole, which is situated in the
centre of this zone.

74. AMPHISCII are the inhabitants of the torrid zone ;
so called, because their shadows fall north or south at
different times of the year ; the sun being sometimes to
the south of them at noon, and at other times to the north.
When the sun is vertical, or in the zenith, which happens
twice in the year, the inhabitants have no shadow, and
are then called ASCII, or shadowless.

75. HETEROSCII is a name given to the inhabitants of
the temperate zones, because their shadows at noon fall
only one way. Thus, the shadow of an inhabitant of the
north temperate zone always falls to the north at noon,
because the sun is then due south ; and the shadow of an
inhabitant of the south temperate zone falls towards the
south at noon, because the sun is due north at that time.

76. PERISCII are those people who inhabit the frigid
zones, so called, because their shadows, during a revolu-
tion of the earth on its axis, are directed towards every
point of the compass. In the frigid zones the sun does
not set during several revolutions of the earth on its axis.

Chap. I. DEFINITIONS, &c. 21

77. ANTCECI are those who live in the same degree of
longitude, and in equal degrees of latitude, but the one in
north and the other in south latitude. They have noon
at the same time, but contrary seasons of the year ; con-
sequently, the length of the days to the one is equal to
the length of the nights to the other. Those who live at
the equator can have no Antceci.

78. PERICECI are those who live in the same latitude,
but in opposite longitudes ; when it is noon with the one,
it is midnight with the other ; they have the same length
of days, and the same seasons of the year. The inha-
bitants of the poles can have no Perioeci.

79. ANTIPODES are those inhabitants of the earth who
live diametrically opposite to each other, and conse-
quently walk feet to feet; their latitudes, longitudes, seasons
of the year, days and nights, are all contrary to each other.

80. The RIGHT ASCENSION of the sun, or of a star, is
that degree of the equinoctial which rises with the sun,
or star, in a right sphere, and is reckoned from the
equinoctial point Aries eastward round the globe.

81. OBLIQUE ASCENSION of the sun, or of a star, is
that degree of the equinoctial which rises with the sun or
star, in an o^lique^phere^ and is likewise counted from the
point Aries eastwararound the globe.

82. OBLIQUE DESCENSION of the sun, or of a star, is
that degree of the equinoctial which sets with the sun or
star in an oblique sphere.

83. The ASCENSIONAL or DESCENSIONAL DIFFER-
ENCE is the difference between the right and oblique
ascension, or the difference between the right arid oblique
descension, and, with respect to the sun, it is the time
he rises before 6 in the spring and summer, or sets before
6 in the autumn and winter.

84. The CREPUSCULUM, or TWILIGHT, is that faint
light which we perceive before the sun rises, and after he
sets. It is produced by the rays of light being refracted
m their passage through the earth's atmosphere, and re-
flected from the different particles thereof. The twilight
is supposed to end in the evening when the sun is 18
degrees below the horizon, or when stars of the sixth
magnitude (the smallest that are visible to the naked eye)

DEFINITIONS, &C.

Part I.

begin to appear; and the twilight is said to begin in the
morning, or it is day-break, when the sun is again within
18 degrees of the horizon. The twilight is the shortest
at the equator, and longest at the poles ; here the sun is
near two months before he retreats 18 degrees below the
horizon, or to the point where his rays are first admitted
into the atmosphere ; and he is only two months more
before he arrives at the same parallel of latitude.

85. REFRACTION. The earth is surrounded by a body
of air, called the ATMOSPHERE, through which the rays
of light come to the eye from all the heavenly bodies ;
and since these rays are admitted through a vacuum, or at
least through a very rare medium*, and fall obliquely
upon the atmosphere, which is a dense medium, they will,
by the laws of optics, be refracted in lines approaching
nearer to a perpendicular from the place of the observer
(or nearer to the zenith) than they would be where the
medium is to be removed. Hence all the heavenly bodies
appear higher than they really are, ' and the nearer they
are to the horizon the greater the refraction, or difference
between their apparent and true altitudes will be; at
noon the refraction is the least. The sun and the moon
appear of an oval figure sometimes near the horizon, by
reason of refraction ; for the under side being more re-
fracted than the upper, the perpendicular diameter will
be less than the horizontal one, which is not affected by
refraction.

c ****»• *«*& ^ich a ray of light can pene-

is culled a medmm, as air, water, oil, glass, &c. The air near

Cliap. I.

DEFINITIONS, &C.

It has long been established, by experiment, that a ray of light pass-
ino1 from a rarer to a denser medium, is refracted towards the denser
medium. Thus, if ABC be the boundary between two media, of which
the lower one is the denser, then a ray of light SB, instead of pursuing
its direction SBWI, is deflected in the direction BE, and a star, instead
cf appearing at s, would appear at e, that is nearer to a perpen-
dicular BP meeting a tangent ft at the point of incidence B. Again,
if DBF be a similar boundary separating the rarer medium contained
between ABC and DEF from the denser medium contained between
DBF and GHI, the ray of light instead of pursuing its new course BE/I
will be again deflected in the direction EH ; and similar effects will
be produced if more media and their boundaries be added. Hence,
a ray of light, instead of being a continued straight line, is broken
into parts BE, EH, HL, inclined to each other at the angles, BEH,
EHL, &c. If we suppose these media to be indefinitely increased and
their boundaries to approach each other by spaces extremely small,
the parts BE, EH, HL, may be considered as curvilinear, and the course
of a ray, instead of being polygonal, will be a curve, concave towards
the denser medium. This may be more adequately represented by the
following figure.

Here the media are
no longer parcelled out
into different strata of
variable density, but
are considered as one
medium of a density
continually varying ;
such is the earth's atmo-
sphere, the most dense
at its surface, and de-
creasing towards the
higher regions. A ray
of light will conse-
quently, in its passage
through the atmosphere,
be deflected into a curve
concave towards the
earth's surface, and will enter a spectator's eye in the direction of a
tangent to that curve ; a star will, therefore, appear in that direction.

Let o be the place of an observer, HOR his horizon, and s a star ;
ADD a section of the earth, formed by a vertical plane passing through
the star at s and the centre (c) of the earth. Here e is the apparent
place of the star, and s its true place ; the angle COK is the apparent
altitude of the star, and the angle SOR its true altitude, the angle eos,
therefore, is the refraction. If the star were at z, the zenith of the

the surface of the earth is more dense than in the higher regions of
the atmosphere ; and beyond the atmosphere, the rays of light are
supposed to meet with little or no resistance.

-24

DEFINITIONS, &C.

Part I.

observer, its height would suffer no refraction. Refraction depends
upon a star's altitude and the heights of the barometer and thermo-
meter : viz. upon the height of the object, and the state of the atmo-
sphere ; hence we sometimes are able to see the tops of mountains,
towers, or spires of churches, which at other times are invisible,
though we stand in the same place. The ancients knew nothing of
refraction, the first who composed a table thereof was Tycho Brake.
The table now in common use was constructed by Dr. Bradley *, or
from his formula, being the result of many trials, conjectures, and
experiments. In the Connaissance des Terns for 1839 there is a
table of refractions, calculated by Messrs. Bouvard and Arago from a
formula by Laplace. (Mechanic Celeste, tome iv. p. 271.)

The sun's meridian altitude on the longest day decreases from the
tropic of Cancer to the north pole ; and in the torrid zone, when the
sun is vertical there is no refraction ; hence the refraction is the least
in the torrid zone, and greatest at the poles. Varenius, in his Geo-
graphy, speaking of the wintering of the Dutch in Nova Zembla, la-
titude 76° north, in the year 1596, says, they saw the sun in the year
1597 six days sooner than they would have seen him, had there been
no refraction.

86. PARALLAX. That part of the heavens in which
a planet would appear, if viewed from the surface of the
earth, is called its apparent place ; and the point in which
it would be seen at the same instant from the centre of
the earth is called its true place : the difference is the pa-
rallax. A star, on account of its great distance from the
earth, has no sensible parallax.

Let c be the centre of
the earth, o the place of an
observer on its surface,
whose sensible horizon is
HOR, and zenith z. Then
if znrwH be a portion of a
vertical circle in the hea-
vens, and s the real place of
any object in the horizon,
if cs be joined and produced
to m it will shew the true
place of s ; the angle WSR or
cso is the parallax. Hence
the altitudes of the celes-
tial bodies are depressed by parallax, which is the greatest at the ho-
rizon, and decrease as the altitude of the object increases ; for the

* The third astronomer royal • he died in the vear 1762.

CJiap. I. DEFINITIONS, &c. 25

angle coy is greater than the angle cos, consequently the angle ovc is
less than the angle osc. At the zenith z the angle ovc vanishes, and
therefore the parallax ceases.

87. ANGLE OF POSITION between two places on the
terrestrial globe is an angle at the zenith of one of the
places; formed by the meridian of that place, and a
vertical circle passing through the other place, being
measured on the horizon from the elevated pole towards
the vertical circle.

THE ANGLE OF POSITION OF A STAR, is an angle formed by two great
circles intersecting each other in the place of the star, the one passing
through the pole of the equinoctial, the other through the pole of the
ecliptic. This angle may be computed from the obliquity of the
ecliptic, and the co-latitude and co-declination of the star ; it is used
in several astronomical calculations. M. Lalande has given a table
of the angles of positions of stars in his Astronomy, I'd edit. vol. i.
page 488. ; and in the Cannaissance des Terns for 1804, there is a table
of the same kind.

88. RHUMBS are the divisions of the horizon into 32
parts, called the points of the compass. The * ancients
were acquainted only with the four cardinal points, and
the wind was said to blow from that point to which it was
nearest.

A Rhumb line, geometrically speaking, is a loxodromic or spiral
curve, drawn or supposed to be drawn upon the earth, so as to cut
each meridian at the same angle, called the proper angle of the rhumb.
If tliis line be continued, it will never return into itself so as to form a
circle, except it happens to be due east and west, or due north and
south ; and it can never be a straight line upon any map, except the
meridians be parallel to each other, as in Mercator's and the plane
chart. Hence the difficulty of finding the true bearing between two
places on the terrestrial globe, or on any map but those above mentioned.
The bearing found by a quadrant of altitude on a globe, is only the
measure of a spherical angle upon the surface of that globe, as deiined
by the angle of position, and not the real bearing or rhumb, as shewn
by the compass ; for, by the compass, if a place A bear due east from a
place B, the place B will bear due west from the place A ; but this is
not the case when measured with a quadrant of altitude.

89. The FIXED STARS are so called because they have
usually been observed to keep the same distance with re-

Pliny's Nat. Hist. Book II. cap. 47.
c

26 DEFINITIONS, &c. Part I.

spect to each other. The stars have an apparent motion
from east to west, in circles parallel to the equinoctial,
arising from the revolution of the earth on its axis, from
west to east : and, on account of the precession of the
equinoxes, their longitudes increase about 50£ seconds in
a year ; this likewise causes a variation in their declin-
ations and right ascensions : their latitudes are also sub-
ject to a small variation.

90. The POETICAL RISING AND SETTING OF THE
STARS, so called because they are taken notice of by the
ancient poets, who referred the rising and setting of the
stars to the sun. THUS, when a star rose with the sun,
or set when the sun rose, it was said to rise and set Cos-
MICALLY. When a star rose at sun-setting, or set with
the sun, it was said to rise and set ACRONICALLY. When
a star first became visible in the morning, after having
been so near the sun as to be hid by the splendour of his
rays, it was said to RISE HELIACALLY ; and when a star
first became invisible in the evening, on account of its
nearness to the sun, it was said to SET HELIACALLY.

91. A CONSTELLATION is an assemblage of stars on
the surface of the celestial globe, circumscribed by the
outlines of some assumed figure, as a ram, a dragon, a
bear, &c. This division of the stars into constellations is
necessary, in order to direct a person to any part of the
heavens where a particular star is situated.

The following tables contain all the constellations on the BRITISH
GLOBES. The ZODIACAL constellations are 1 2 in number, the NORTHERN
constellations 35, and the SOUTHERN 49, making in the whole 96. By
adding together the numbers of stars in the first columns of the follow-
ing tables, the total will be found to be 2930 ; of this number there
are only 19 of the first magnitude, and 422 cannot be seen at London.
The largest stars are called stars of the first magnitude. Those of the
sixth magnitude are the smallest that can be seen by the naked eye.
The figures on the left hand of the tables show the number of stars in
each constellation as given in the Royal Astronomical Society's Cata-
logue. Rt. Asc. denotes the right ascension, Dec. the declination of
near the middle of the several constellations, for the ready finding them
on the globe.

Chap. I. DEFINITIONS, &c. 27

I. CONSTELLATIONS IN THE ZODIAC.

£ J3 Names of the Constellations, and of the principal Stars

in each, with their Magnitudes.
£^ RtAsc. Dec.

65. Aries, The Ram, a. Arietis 3. - - 34. 18 N.
160. Taurus, The Bull, a. Aldebaran 1, the Pleiades and

Hyades, - - - - 62. 18 N.

83. Gemini, The Twins, o2 Castor 3, ft Pollux 2, 106. 25 N.

71. Cancer, The Crab, Acubene 4, or ft 4, - 128. 20 N.

96. Leo, 7%eLzow,aRegulusorCorLeonisl,Deneb2,155. 15 N.
123. Virgo, The Virgin, a Spica Virginis 1, e Vende-

miatrix 2, - - - 1 92. 3 N.

61. Libra, The Balance, Zubenich Meli 2, or ft Librae, 225. 15 S.

63. Scorpio, The Scorpion, a. Antaresl, or a Scorpii, 242. 26 S.

136. Sagittarius, The Archer, a- Sagittarii 3, - 285. 32 S.

81. Capricornus, The Goat, a Capricorni 3, - 312. 20 S.

139. Aquarius, The Water Bearer, J Scheat 3 and 03, 332. 9 S.

123. Pisces, The Fishes, - - - 5. 10 N.

II. THE NORTHERN CONSTELLATIONS.

25. Andromeda, o Alpherat 1, or ft Mirach 2, 15. 35 N.

57. Aquila, The Eagle, with Antinous, o Atair 1, 291. 10 N.

36. Auriga, The Charioteer or Waggoner, a. Capella 1, 77. 42 N.

48. Bootes, o Arcturus 1, € Bootis 3, - - 216. 30 N.

13. Camelopardalus, The Camelopard, - - 70. 68 N.

5. Canes Venatici, and Cor Caroli, Charles's Heart,

Asterion and Chara, - - 195. 40 N.

— Caput Medusae, The Head of Medusa, See Perseus, 43. 37 N.

19. Cassiopea, The Lady in her Chair, Schedar 8, 14. 60 N.

25. Cepheus, Alderamin 3, - - 325. 65 N.

Cerberus, The Three-headed Dog, See Hercules 271. 18 N.

9. Clypeum vel Scutum Sobieski, SobieskVs Shield, 275. 15 S.

36. Coma Berenices, Berenice's Hair, - 188. 26 N.

13. Corona Borealis, The Northern Crown, Alphacca 2, 234. 30 N.

38. Cygnus, The Swan, Deneb 1, - - 304. 42 N.

16. Delphinus, The Dolphin, - 308. 15 N.

40. Draco, The Dragon, ft 2, and 7 2, - - 270. 66 N.

11. Equulus, The Little Horse, - - 316. 6 N.

73. Hercules and Cerberus, Ras Algethi 3, - 252. 27 N.

6. Lacerta, The Lizard ... 336. 44 N.
11. Leo Minor, The Little Lion, - - 151. 36 N.

8. Lynx, The Lynx, - - - - 111. 50 N.

10. Lyra, The Harp, a Vega 1 , - 280. 35 N.

11. Mons Moenalus*, The Mountain Mo2nalus, - 225. 3 N.

* Some of the stars in Mons Moenalus are in the Astronomical
Society's Catalogue assigned to Virgo and some to Serpens.
C 2

DEFINITIONS, &c. Part I.

Names of the Constellations, and of the principal Stars
in each, with their Magnitudes.

Rt.Asc. Dec.

6. Musca, The Fly, in Ast. S. Cat. in Aries, - 40. 27 N.

81. Pegasus, The Flying Horse, a Markab2, 7 Scheat 2, 340. 1 5 N!

23. Perseus, and Caput Medusa, a Persei 2, ft Algol 2, 46. 47 N.

15. Sagitta, The Arrow, - - - 295. 18 NT!

57. Serpens, The Serpent, - - - 234. 10 N.

-J- Serpentarius, The Serpent Bearer, See Ophiucus 260. 0

4. Taurus Poniatowski, The Bull of Poniatowski, 275, 5 N.

5. Triangulum, The Triangle, - - 29. 32 N.
5. Triangulum Minus, The Little Triangle, - 32. 29 N.

29. Ursa Major, The Great Bear, Duhbe 1, Alioth 2, 153. 58 N.'
10. Ursa Minor, The Little Bear, a Polaris or the Polar

Star, or Alrukabah, 2, 235. 78 N.

31. Vulpecula et Anser, The Fox and Goose, - 300.' 25 N.'

10. Tarandus, The Rein-Deer, - - - 45. 77 N.
To the preceding list of northern constellations, foreign mathe-
maticians have added Le Messier, Taurus Regalis, Frederick's Ehre
Frederick's Glory, Tubus Herschellii Major, HerscheFs Great Telescope.

III. THE SOUTHERN CONSTELLATIONS.

7. Antlia Pneumatica, The Air Pump, - 150' 355

8. Apparatus Sculptoris . . . 5 32 S*

3. Apus vel Avis Indica, The Bird of Paradise, 245. 76 s'
8. Ara, The Altar, - - . „ 256 54 S*

84. Argo Navis, The Ship Argo, a Canopus 1, - 115* 50 S.'

6. -erandenburgium Sceptrum, - . gy 15 S

4. Gela Sculptoris, The Engraver s Tools, - 68.' 42 S.'
38. Cams Major, The Great Dog, a Siriusl, - 100. 24 S.
14. Cams Minor, The Little Dog, a Procyon 1, 112. 5 N.
36. Centaurus, The Centaur, - . ]<K if o

106. Cetus, The Whale, Mencar 2, - ff f! o

8. Chameleon, The Cameleon, . l

, ^..^ ^Up ur u-o^er Alices 3, - ifis ic G

7. Crux, 2%e Cross, -

6. Dorado or Xiphias, The Sword Fish,

1. Equuleus Pictoris, The Painter's Easel, - 80 55 S

83. Eridanus, The River Po, a Achernar 1,' . 60* ^}O S*

-U. I'ornax Chemica, The Chemist's Furnace
12. Grus. The Craw. _ ' ^^. JO &.

Horologium, T^e C/oc^, . ™

Indus, Me Indian *3 70 S'

Chap. I. DEFINITIONS, &c. 29

.1 « Names of the Constellations, and of the principal Stars

I ^ in each, with their Magnitudes.

£<fc» Rt.As. Dec.

25. Lupus, The Wolf, - - - - 230. 45 S.

1. Microscopium, The Horoscope, - - 310. 37 S.

24. Monoceros, TAe Unicorn, - - - 110. 2 S.

4. Musca Australis vel Apis, The Southern Fly, 185. 68 S.
3. Norma vel Quadra Euclidis, Euclid's Square 242. 45 S.
6. Octans, 310. 80 S.

74. Ophiuchus, formerly called Serpentarius, - 260. 0

75. Orion, o Betelgeux 1, )8 Rigel 1, 7 Bellatrix 2, 82. 0
12. Pavo, The Peacock, - - - 802. 68 S.
15. Phoenix, A Fabulous Bird, - - 10. 50 S.
1 5 . Piscis Australis, The Southern Fish, a Fomalhaut 1 , 335. 32 S.

6. Piscis Volans, The Flying Fish, - ; - 127. 68 S.

11. Pixis Nautica, The Mariner's Compass, - 132. 30 S.
— Praxiteles, See ca?la Sculptoris, - - 68. 42 S.

7. Reticulus Rhomboidalis, The Rhomboidal Net, 60. 62 S.

12. Robur Caroli, Charles's Oak, - - 159. 60 S.
35. Sextans, The Sextant, - - - 155. 0

5. Solitarius, An Indian Bird, - - 210. 21 S.
5. Telescopiura, The Telescope, - - 278. 53 S.
9. Tucan Touchan, The American Goose, - 359. 66 S.
5. Triangulura Australis, The Southern Triangle, 238. 65 S.
Foreign mathematicians have added to the preceding list of southern

constellations, Psalterium Georgianum, The Georgian Psaltery ; Tubus
Herschelii Minor, Herschel's Less Telescope ; Montgolfier's Balloon ;
the Press of Guttenbergh ; and the Cat.

Explanation of the different emblematical Figures delineated on the
Surface of the Celestial Globe.

I. THE CONSTELLATIONS IN THE ZODIAC.

It is conjectured that the figures in the signs of the zodiac are de-
scriptive of the seasons of the year, and that they are Chaldean or
Egyptian hieroglyphics, intended to represent some remarkable occur-
rence in each month. Thus the spring signs were distinguished for
the production of those animals which were held in the greatest esteem,
viz. the sheep, the black cattle, and the goats ; the latter being the most
prolific, were represented hy the figure of Gemini. — When the sun
enters Cancer, he discontinues his progress towards the north pole, and
begins to return back towards the south pole. This retrograde motion
was represented by a Crab, which is said to go backwards. The heat
that usually follows in the next month is represented by the Lion, an
animal remarkable for its fierceness, and which, at this season, was
frequently impelled, through thirst, to leave the sandy desert and make
its appearance on the banks of the Nile. The sun entered the 6th sign
about the time of harvest, which season was therefore represented by a
virgin or female reaper, with an ear of corn in her hand. When the

c 3

30 DEFINITIONS, &c. Parti.

sun enters Libra, the days and nights are equal all over the world,
and seem to observe an equilibrium, like a balance.

Autumn, which produces fruits in great abundance, brings with it
a variety of diseases ; this season is represented by that venomous
animal the Scorpion, who wounds with a sting in his tail as he recedes.
The fall of the leaf was the season for hunting, and the stars which
marked the sun's path at tliis time were represented by a huntsman, or
archer, with his arrows and weapons of destruction.

The Goat, which delights in climbing and ascending some moun-
tain or precipice, is the emblem of the winter solstice, when the sun
begins to ascend from the southern tropic, and gradually to increase
in height for the ensuing half year.

Aquarius, or the Water-bearer, is represented by the figure of a
man pouring out water from an urn, an emblem of the dreary and un-
comfortable season of winter.

The last of the zodiacal constellations was Pisces, or a couple of
fishes tied back to back, representing the fishing-season. The severity
of the winter is over, the flocks do not afford sustenance, but the seas
and rivers are open, and abound with fish.

The Chaldeans and Egyptians were the original inventors of astro-
nomy ; they registered the events in their history, and the mysteries of
their religion among the stars by emblematical figures. The Greeks
displaced many of the Chaldean constellations, and placed such images
as had reference to their own history in their room. The same method
was followed by the Romans ; hence the accounts given of the signs
of the zodiac, and of the constellations, are contradictory and involved
in fable.

II. THE NORTHERN CONSTELLATIONS.

ANDROMEDA is represented on the celestial globe by the figure of
a woman almost naked, having her arms extended, and chained by
the wrist of her right arm to a rock. She was the daughter of Ce-
plieus, king of Ethiopia, who, in order to preserve his kingdom, was
obliged to tie her naked to a rock near Joppa, now Jaffa, in Syria, to
be devoured by a sea-monster ; but she was rescued by Perseus, in his
return from the conquest of the Gorgons, who turned the monster into
a rock by shewing it the head of Medusa. Andromeda was made a
constellation after her death, by Minerva.

ANTINODS was a youth of Bithynia, in Asia Minor, a great favourite
3f the emperor Adrian, who erected a temple to his memory, and
placed him among the constellations. -Antinous is generally reckoned
a part of the constellation Aquila.

AQUILA is supposed to have been Merops, a king of the island of
.os, one of the Cyclades; who, according to Ovid, was changed into
an eagle, and placed among the constellations

ASTERION ET CHARA, vel CANES VENATICX, the two greyhounds, held
m a string by Bootes , they were formed by Hevelius oui of the Stdl*
Informes of the ancient catalogues.

Chap. I. DEFINITIONS, &c. 31

AURIGA is represented on the celestial globe by the figure of a man
in a kneeling or sitting posture, with a goat and her kids in his left
hand, and a bridle in his right. The Greeks give various accounts of
this constellation ; some suppose it to be Erichthonius, the fourth king
of Athens, and son of Vulcan and Minerva ; he was very deformed,
and his legs resembled the tails of serpents ; he is said to have invented
chariots, and the manner of harnessing horses to draw them. Others
say that Auriga is Mirtilus, a son of Mercury and Phaetusa ; he was
charioteer to CEnomaus, king of Pisa, in Elis, and so experienced in
riding and the management of horses, that he rendered those of (Eno-r
maus the swiftest in all Greece ; his infidelity to his master proved at
last fatal to him, but being a son of Mercury, he was made a constella-
tion after his death. But as neither of these fables seem to account for
the goat and her kids, it has been supposed that they refer to Amalthsea,
daughter of Melissus, king of Crete, who, in conjunction with her sister
Melissa, fed Jupiter with goats' milk ; it is moreover said that Amal-
thaea was a goat called Olenia, from its residence at Olenus, a town of
Peloponnesus.

BOOTES is supposed to be Areas, the son of Jupiter and Calisto ; Juno,
who was jealous of Jupiter, changed Calisto into a bear ; she was near
being killed by her son Areas in hunting. Jupiter, to prevent farther
injury from the huntsmen, made Calisto a constellation of heaven, and
on the death of Areas, conferred the same honor on him. Bootes is
f represented as a man in a walking posture, grasping in his left hand
' a club, and having his right hand extended upwards, holding the cord
of the two dogs Asterion and Chara, which seem to be barking at the
Great Bear ; hence Bootes is sometimes called the bear-driver, and
the office assigned him is to drive the two bears round about the pole .
& CAMELOPARDALUS was formed by Hevelius. The Camelopard is
jpmarkably tame and tractable ; its natural properties resemble those
of the camel, and its body is variegated with spots like the leopard.
This animal is to be found in Ethiopia and other parts of Africa ; its
neck is about seven feet long, its fore and hind legs from the hoof to
the second joint, are nearly of the same length ; but from the second
joint of the legs to the body, the fore legs are so long in comparison
with the hind ones, that the b6dy seems to slope like the roof of a house.

CASSIOPEIA was the wife of Cepheus, and mother of Andromeda.
See these constellations, as also Cetus.

CEPHEUS was a king of ^Ethiopia, and the father of Andromeda by
Cassiopeia ; Cepheus was one of the Argonauts, who went with Jason
to Colchis to fetch the golden fleece.

CERBERUS was a dog belonging to Pluto, the god of the infernal
regions ; this dog had fifty heads, according to Hesiod, and three ac-
cording to other mythologists ; he was stationed at the entrance of the
infernal regions, as a watchful keeper, to prevent the living from
entering, and the dead from escaping from their confinement. The
last and most dangerous exploit of Hercules, was to drag Cerberus
from the infernal regions, and bring him before Eurystheus, king of
Argos.

32 DEFINITIONS, &c. Part I.

COMA BERENICES is composed of the unformed stars, between the
Lion's tail and Bootes. Berenice was the wife of Evergetes, a sur-
name signifying benefactor ; when he went on a dangerous expedition,
she vowed to dedicate her hair to the goddess Venus, if he returned in
safety. Some time after the victorious return of Evergetes, the locks
which were in the temple of Venus disappeared ; and Conon, an as-
tronomer, publicly reported that Jupiter had carried them away, and
made them a constellation.

COR CAROLI, or Charles's heart, in the neck of Chara, the southern-
most of the two dogs held in a string by Bootes, was so denominated
by Sir Charles Scarborough, physician to king Charles II. in honour
of king Charles I.

CORONA BOREALIS is a beautiful crown given by Bacchus, the son
of Jupiter, to Ariadne, the daughter of Minos, second king of Crete.
Bacchus is said to have married Ariadne after she was basely deserted
by Theseus, king of Athens, and after her death the crown which
Bacchus had given her was made a constellation.

CYGNUS is fabled by the Greeks to be the swan under the form of
which Jupiter deceived Leda, or Nemesis, the wife of Tyndarus, king
of Laconia. Leda was the mother of Pollux and Helena, the most
beautiful woman of the age ; and also of Castor and Clytemnestra.
The two former were deemed the offspring of Jupiter, and the others
claimed Tyndarus as their father.

DELPHINUS, the dolphin, was placed among the constellations by
Neptune, because, by means of a dolphin, Amphitrite became the wife
of Neptune, though she had made a vow of perpetual celibacy.

DRACO. The Greeks give various accounts of this constellation ;
by some it is represented as the watchful dragon which guarded the
golden apples in the garden of the Hesperides, near mount Atlas in
Africa ; and was slain by Hercules : Juno, who presented these apples
to Jupiter on the day of their nuptials, took Draco up to heaven, and
made a constellation of it as a reward for its faithful services : others
maintain that in a war with the giants, this dragon was brought into
combat, and opposed to Minerva, who seized it in her hands and threw
it, twisted as it was, into the heavens round the axis of the earth, before
it had time to unwind its contortions.

EQUULUS, the little horse, or Equi Sectio, the horse's head, is sup-
posed to be the brother of Pegasus.

HERCULES is represented on the celestial globe holding a club in
his right hand, the three-headed dog Cerberus in his left, and the skin
of the Nemaean lion thrown over his shoulders. Hercules was the
son of Jupiter and Alcmena, and reckoned the most famous hero in
antiquity.

LACERTA, the lizard, was added by Hevelius to the old constellations.

LEO MINOR was formed out of the Stella: Informes, or unformed stars
of the ancients, and placed above LEO the zodiacal constellation.
According to the Greek fables, LEO was the celebrated Nemajan lion
which had dropped from the moon, but being slain by Hercules, was
elevated to the heavens by Jupiter, in commemoration of the dreadful

Chap. I. DEFINITIONS, &c. 33

conflict, and in honour of that hero. But this constellation was amongst
the Egyptian hieroglyphics, long before the invention of the fables of
Hercules. See the Zodiacal Constellations, p. 27. Nemaea was a
town of Argolis in Peloponnesus, and was infested by a lion which
Hercules slew, and clothed himself in the skin ; games were instituted
to commemorate this great event.

The LYNX was composed by Hevelius out of the unformed stars of
the ancients, between Auriga and Ursa Major.

LYRA, the lyre or harp, is included in Vultur Cadens. This con-
stellation was at first a tortoise, afterwards a lyre, because the strings
of the lyre were originally fixed to the shell of a tortoise : it is as-
serted that this is the lyre which Apollo or Mercury gave to Orpheus,
and with which he descended the infernal regions, in search of his
wife Eurydice. Orpheus after death received divine honours, the
Muses gave an honourable burial to his remains, and his lyre became
one of the constellations.

MONS M^ENALUS. The mountain Maenalus in Arcadia was sacred
to the god Pan, and frequented by shepherds ; it received its name
from Maenalus, a son of Lycaon, king of Arcadia.

PEGASUS, the winged horse, according to the Greeks, sprung from
the blood of the Gorgon Medusa, after Perseus, a son of Jupiter, had
cut off her head. Pegasus fixed his residence on mount Helicon in
Boeotia, where, by striking the earth with his foot, he produced a foun-
tain called Hippocrene. He became the favourite of the Muses, and
being afterwards tamed by Neptune, or Minerva, he was given to Bel-
lerophon to conquer the Chimaera, a hideous monster that continually
vomited flames ; the fore-parts of its body were those of a lion,
the middle was that of a goat, and the hinder-parts were those of a
dragon ; it had three heads, viz. that of a lion, a goat, and a dragon.
After the destruction of this monster, Bellerophon attempted to fly
to heaven upon Pegasus, but Jupiter sent an insect which stung
the horse, so that he threw down the rider. Bellerophon fell to the
earth, and Pegasus continued his flight up to heaven, and was placed
by Jupiter among the constellations.

PERSEUS is represented on the globe with a sword in his right hand,
the head of Medusa in his left, and wings at his ancles. Perseus was
the son of Jupiter and Danae. Pluto, the god of the infernal regions,
lent him his helmet, which had the power of rendering its bearer invi.
sible ; Minerva, the goddess of wisdom, furnished him with her buck-
ler, which was resplendent as glass ; and he received from Mercury
wings, and a dagger or sword ; thus equipped, he cut off the head of
Medusa, and from the blood which dropped from it in his passage
through the air, sprang an incalculable number of serpents, which
ever after infested the sandy deserts of Libya. Medusa was one of the
three Gorgons who had the power to turn into stone all those on whom
they fixed their eyes ; Medusa was the only one subject to mortality :
she was celebrated for the beauty of her locks, but having violated the
sanctity of the temple of Minerva, that goddess changed her locks into
serpents. See the constellation Andromeda.

3$ DEFINITIONS, &c. Part I.

SAGITTA, the arrow. The Greeks say that this constellation owes
its origin to one of the arrows of Hercules, with which he killed the
eagle or vulture that perpetually gnawed the liver of Prometheus, who
was tied to a rock on Mount Caucasus, by order of Jupiter.

SCUTUM SOBIESKI was so named by Hevelius, in honour of John
Sobieski, king of Poland. Hevelius was a celebrated astronomer, bora
at Dantzick : his catalogue of fixed stars was entitled Firmamentum
Sobieskianum, and dedicated to the king of Poland.

SERPENS is also called Serpens OphiucM, being grasped by the hands
of Ophiuchus.

SERPENTARIUS, Ophiuchus, or JEsculapius, is represented with a
large beard, and holding in his two hands a serpent. The serpent was
the symbol of medicine, and of the gods who presided over it, as
Apollo and ^Esculapius, because the ancient physicians used serpents
in their prescriptions.

TAURUS PONIATOWSKI was so called in honour of Count Ponia-
tx>wski, a Polish officer of extraordinary merit, who saved the life of
Charles XII. of Sweden, at the battle of Pultowa, a town near the
Dnieper, about 150 miles south-east of Kiov ; and a second time at
the island of Rugen, near the mouth of the river Oder.

TRIANGULUM. A triangle is a well known figure in geometry ; it
was placed in the heavens in honour of the most fertile part of Egypt,
being called the delta of the Nile, from its' resemblance to the Greek
letter of that name A. The invention of geometry is usually ascribed
to the Egyptians, and it is asserted that the annual inundations of the
Nile, which swept away the bounds and land-marks of estates, gave
occasion to it, by obliging the Egyptians to consider the figure and
quantity belonging to the several proprietors.

URSA MAJOR is said to be Calisto, an attendant of Diana, the god-
dess of hunting. Calisto was changed into a bear by Juno. — See the
constellation Bootes. — It is farther stated that the ancients represented
Ursa Major and Ursa Minor, each under the form of a waggon, drawn
by a team of horses. Ursa Major is well known to the country people
at this day, by the title of Charles's Wain, or waggon : in some
places it is called the plough. There are two remarkable stars in Ursa
Major, considered as the hindmost in the square of the wain, called the
pointers, because an imaginary line drawn through these stars, and
extended upwards, will pass near the pole-star in the tail of the Little Bear.

VULPECULA ET ANSER, the Fox and the Goose, was made by Heve-
lius out of the unformed stars of the ancients.

III. THE SOUTHERN CONSTELLATIONS.

ARA is supposed to be the altar on which the gods swore before
their combat with the giants.

ARGO NAVIS is said to be the ship Argo, which earned Jason and
the Argonauts to Colchis to fetch the golden fleece.

CAN is MAJOR, the Great Dog, according to the Greek fables, is
one of Orion's hounds ; (See Canis Minor ;) but the Egyptians, who
carefully watched the rising of this constellation, and by it judged of

Chap. I. DEFINITIONS, &c. 35

the swelling of the Nile, called the bright star Sirius the centinel and
watch of the year ; and according to their hieroglyphical manner of
writing, represented it under the figure of a dog. The Egyptians
called the Nile Siris, and hence is derived the name of their deity
Oiirit,

CANIS MINOR, the Little Dog, according to the Greek fables, is
one of Orion's hounds ; but the Egyptians were most probably the
inventors of this constellation, and as it rises before the dog-star,
which at a particular season was so much dreaded, it is properly re-
presented as a little watchful creature, giving notice of the other's
approach ; hence the Latins have called it Antecanis, the star before
the dog.

CENTAURUS. The Centauri were a people of Thessaly, half men
and half horses. The Thessalians were celebrated for their skill in
taming horses, and their appearance on horseback was so uncommon
a sight to the neighbouring states, that at a distance they imagined
the man and horse to be one animal : when the Spaniards landed in
America, and appeared on horseback, the Mexicans had the same
ideas. Tlu's constellation is by some supposed to represent Chiron
the Centaur, tutor of Achilles, JEsculapius, Hercules, &c. ; but as
Sagittarius is likewise a Centaur, others have contended that Chiron is
represented by Sagittarius.

GET as, the whale, is pretended by the Greeks to be the sea-monster
which Neptune, brother to Juno, sent to devour Andromeda ; because
her mother, Cassiopeia, had boasted herself to be fairer than Juno and
the Nereides.

CORVCJS, the crow, was according to the Greek fables made a con-
stellation by Apollo : this god being jealous of Coronis, (the daughter
of Phlegyas and mother of ^Esculapius,) sent a crow to watch her
behaviour ; the bird, perched on a tree, perceived her criminal par-
tiality to Ischys, the Thessalian, and acquainted Apollo with her conduct.

CRUX, CRUSERO or CROSIER. There are four stars in this constel-
lation forming a cross, by which mariners sailing in the southern
hemisphere readily find the situation of the Antarctic pole.

ERIDANUS, the river Po, called by Virgil the king of rivers, was
placed in the heavens for receiving Phaeton, whom Jupiter struck
with thunder-bolts when the earth was threatened with a general con-
flagration, through the ignorance of Pha?ton, who had presumed to
be able to guide the chariot of the sun. The Po is sometimes called
Orion's river.

HYDRA is the water serpent, which, according to poetic fable, in-
fested the lake Lerna in Peloponnesus : this monster had a great
number of heads, and as soon as one was cut off, another grew in
its stead : it was killed by Hercules. The general opinion is, that this
Hydra was only a multitude of serpents which infested the marshes of
Lerna.

LEPUS, the hare, according to the Greek fables, was placed near
Orion, as being one of the animals which he hunted.

MICROSCOPIUM, the microscope, is an optical instrument composed

36 DEFINITIONS, &c. Part I. '

of lenses or mirrors, so arranged as to render very minute objects clear
and distinct.

MONOCEROS, the unicorn, was added by Hevelius, and composed
of stars which the ancients had not comprised within the outlines of the
other constellations.

ORION is represented on the globe by the figure of a man with a
sword in his belt, a club in his right hand, and the skin of a lion in
his left ; he is said by some authors to be the son of Neptune and
Euryale, a famous huntress ; he possessed the disposition of his mother,
became the greatest hunter in the world, and boasted that there was
not any animal on the earth which he could not conquer. Others say,
that Jupiter, Neptune, and Mercury, as they travelled over Bceotia,
met with great hospitality from Hyrieus, a peasant of the country, who
was ignorant of their dignity and character. When Hyrieus had dis-
covered that they were gods, he welcomed them by the voluntary sacri-
fice of an ox. Pleased with his piety, the gods promised to grant him
whatever he required, and the old man, who had lately lost his wife,
and to whom he made a promise never to many again, desired them,
that as he was childless, they would give him a son without obliging
him to break his promise. The gods consented, and Orion was pro-
duced from the hide of the ox.

PISCIS AUSTRALIS, the southern fish, is supposed by the Greeks to
be Venus, who transformed herself into a fish, to escape from the ter-
rible giant Typhon.

ROBUR CAROLI, or Charles's Oak, was so called by Dr. Halley, in
memory of the tree in which Charles II. saved himself from his pur-
suers after the battle of Worcester. Dr. Halley went to St. Helena,
in the year 1676, to take a catalogue of such stars as do not rise above
the horizon of London.

SEXTANS, the sextant, a mathematical instrument well known to
mariners, was formed by Hevelius from the Stettce Informes of the
ancients.

92. GALAXY, VIA LACTEA, or Milky-way, is a whitish
luminous tract which seems to encompass the heavens,
like a girdle, of a considerable though unequal breadth,
varying from about 4 to 20 degrees. It is composed of
an infinite number of small stars, which by their joint
light occasion that confused whiteness which we perceive
m a clear night when the moon does not shine very
brightly. The milky-way may be traced on the celestial
globe, beginning at Cygnus, through Cepheus, Cassio-
peia, Perseus, Auriga, Orion's club, the feet of Gemini,
part of Monoceros, Argo Navis, Robur Caroli, Crux,
tne teet of the Centaur, Circinus, Quadra Euclidis, and
Ara ; here it is divided into two parts; the eastern branch

Chap. I. DEFINITIONS, &c. 37

passes through the tail of Scorpio, the bow of Sagittarius,
Scutum Sobieski, the feet of Antindus, Aquila, Sagitta,
and Vulpecula; the western branch passes through the
upper part of the tail of Scorpio, the right side of Ser-
pentarius, Taurus, Poniatowski, the Goose, and the neck
of Cygnus, and meets the aforesaid branch in the body of
Cygnus.

93. NEBULOUS, or cloudy, is a term applied to certain
fixed stars, smaller than those of the 6th magnitude,
which only shew a dim hazy light like little specks or
clouds. In Praesepe in the breast of Cancer are reckoned
36 little stars ; F. le Compte adds, that there are 40 such
stars in the Pleiades, and 2500 in the whole Constellation
of Orion. It may be further remarked, that the Milky-
way is a continued assemblage of Nebulae.

94. BAYER'S CHARACTERS. John Bayer of Augsburg
in Swabia, published in 1603 an excellent work, entitled
Uranometria, being a complete atlas of all the constel-
lations, with the useful invention of denoting the stars in
every constellation by the letters of the Greek and
Roman Alphabets ; setting the first Greek letter a to the
principal star in each constellation, ft to the second in
magnitude, y to the third, and so on, and when the
Greek alphabet was finished, he began with a, b, c, &c.
of the Roman. This useful method of describing the
stars has been adopted by all succeeding astronomers,
who have farther enlarged it by adding the numbers,
1, 2, 3, &c. in the same regular succession, when any
constellation contains more stars than can be marked by
the two alphabets. The figures are, however, some-
times placed above the Greek letter, especially where
double stars occur ; for though many stars may appear
single to the naked eye, yet when viewed through a
telescope of considerable magnifying power they appear
double, triple, &c. Thus, in Dr. Zach's Tabulae Motuum
Soils, we meet with f Tauri, 0 Tauri, y Tauri, Sl Tauri,
S2 Tauri, &c. The most complete catalogue of the fixed
stars is published by the Royal Astronomical Society.

As the Greek letters so frequently occur in catalogues of the stars
and on the celestial globes, the Greek alphabet is here introduced for
the use of those who are unacquainted with the letters. The capitals

DEFINITIONS, &C.

Part I.

are seldom used in the catalogues of stars, but are here given for the
sake of regularity.

THE GREEK ALPHABET.

Name.

Sound.

Alpha

# 6

Beta

v T

Gamma

Delta

Epsilon

e short

Zeta

Eta

elong

&fl

Theta

Iota

Kappa
Lambda

k
1

Name.

Sound.

O micron

o short

Rho

Sigma

Tau

Upsilon

Phi

Chi

Psi

Omega

o long.

95. Planets are erratic opaque bodies resembling our
earth, and, having no light of their own, shine only by
reflecting the light of the sun. They are divided into
three classes, viz. Primary Planets, Minor Primary Pla-
nets, and Secondary Planets, commonly called Satellites
or Moons.

96. The PRIMARY PLANETS are those which revolve
round the sun as a centre : they are seven in number :
their order in the system, and the names and characters
by which they are expressed being as follows: Mercury £ ,
Venus ?, Earth Q, Mars <?, Jupiter If, Saturn T?, and
Uranus $, called also the Georgium Sidus, or Herschel.

97. The MINOR PRIMARY PLANETS are four in num-
ber: they revolve round the sun as a centre, between the
orbits of Mars and Jupiter, but are distinguished from
the primary planets by their diminutive size, and by the
form and position of their orbits. Their names and cha-
racters are Vesta S, Juno t, Ceres ?, and Pallas 0.

Superior and inferior, or exterior and interior, are
relative terms applied to the primary and minor primary
planets: those being called superior or exterior, which
are farther from the sun ; and those inferior or interior,
which are nearer to him: thus, in respect of our earth,
Mercury and Venus are inferior planets, and the rest are
superior. Mercury being the nearest planet to the sun.
and Uranus the most remote from him, may be considered,
the former as the inferior planet of the system, and the
latter the superior.

Chap. 1. DEFINITIONS, &c. 39

98. The SECONDARY PLANETS are those bodies which
revolve round their respective primaries as their centre of
motion, in the same manner as the primary planets circulate
round the sun. The number of satellites at present known
is eighteen ; viz. the Moon ) , which attends on our earth,
four belonging to Jupiter, seven to Saturn, and six to
Uranus.

99. The ORBIT of a planet is the imaginary path it
describes round the sun.

100. NODES are the two opposite points where the
orbit of a planet seems to intersect the ecliptic. That
where the planet appears to ascend from the south to the
north side of the ecliptic is called the ascending or north
node, and is marked thus & ; and the opposite point
where the planet appears to descend from the north to
the south is called the descending or south node, and is
marked ?5.

101. ASPECT of the stars or planets is their situation
with respect to each other. There are five aspects, viz.
$ Conjunction, when they are in the same sign and de-
gree ; 4f Sextile, when they are two signs, or a sixth part
of a circle, distant ; Q Quartile, when they are three signs,
or a fourth part of a circle, from each other ; A Trine,
when they are four signs, or a third part of a circle, from
each other ; § Opposition, when they are six signs, or
half a circle from each other.

The conjunction and opposition (particularly of the
moon) are called the Syzygies, and the quartile aspect,
the Quadratures,

102. DIRECT. A planet's motion is said to be direct,
when it appears (to a spectator on the earth) to go for-
ward in the zodiac, according to the order of the signs.

103. STATIONARY. A planet is said to be stationary
when (to an observer on the earth) it appears for some
time in the same point of the heavens.

104. RETROGRADE. A planet is said to be retrograde,
when it apparently goes backward, or contrary to the
order of the signs.

105. DIGIT, the twelfth part of the sun or moon's ap-
parent diameter.

106. Disc, the face of the sun or moon, such as they
appear to a spectator on the earth ; for though the sun

40 DEFINITIONS, &C.

and moon be really spherical bodies, they appear to be
circular planes. t

107. GEOCENTRIC latitudes and longitudes of the
planets are their latitudes and longitudes, as seen from
the earth.

108. HELIOCENTRIC latitudes and longitudes of the
planets are their latitudes and longitudes, as they would
appear to a spectator situated in the sun.

109. APOGEE, or Apogaeum, is that point in the orbit
of a planet, the moon, &c. which is farthest from the
earth.

110. PERIGEE, or Perigaeum, is that point in the orbit
of a planet, the moon, &c. which is nearest to the earth.

111. APHELION, or Aphelium, is that point in the or-
bit of the earth, or of any other planet, which is farthest
from the sun. This point is called the higher Apsis.

1 12. PERIHELION, or Perihelium, is that point in the
orbit of the earth, or of any other planet, which is nearest
to the sun. This point is called the lower APSIS.

113. LINE OF THE APSIDES is a straight line joining
the higher and lower apsis of a planet ; viz. a line joining
the Aphelium and Perihelium.

114-. ECCENTRICITY of the orbit of any planet is the
distance between the sun and the centre of the planet's
orbit.

115. OCCULT ATION is the obscuration or hiding from
our sight any star or planet, by the interposition of the
body of the moon, or of some other planet.

1 16. TRANSIT is the apparent passage of any planet
over the face of the sun, or over the face of another
planet. Mercury and Venus, in their transits over the
sun's disc, appear like dark specks.

1 17. ECLIPSE OF THE SUN is an occultation of part of
the face of the sun, occasioned by an interposition of the
moon between the earth and the sun ; consequently all
eclipses of the sun happen at the time of new moon.

1 18. ECLIPSE OF THE MOON is a privation of the light
of the moon, occasioned by an interposition of the earth
between the sun and the moon; consequently all eclipses
of the moon happen at full moon.

119. ELONGATION of a planet is the angle formed by

Chap. I.

DEFINITIONS, &C.

two lines drawn from the earth, the one to the sun, and
the other to the planet.*

120. DIURNAL ARC is the arc described by the sun,
moon, or stars, from their rising to their setting. — The
sun's semi-diurnal arc is the arc described in half the
length of the day.

121. NOCTURNAL ARC is the arc described by the sun,
moon, or stars, from their setting to their rising.

122. ABERRATION is an apparent motion of the celes-
tial bodies, occasioned by the earth's annual motion in its
orbit, combined with the progressive motion of light.

To illustrate this definition, — If light be supposed to have a pro-
gressive motion, the position of the telescope through which a star is
viewed must be different from that which it would have been, if light
had been instantaneous, and therefore the situation of a star measured
in the heavens, will be different from its true situation. Let .jf repre-
sent the situation of a fixed star, A B the direction of the earth's mo-
tion, Ji B the direction of a particle of light, entering the axis mo of
a telescope at o, and moving through o B whilst the earth moves from
ra to B, then if the telescope be kept parallel to itself, the light will de-
scend in the axis.

For, let the axis nd, ve continue pa-
rallel to mo, then if each motion be
considered as uniform, (that of the spec-
tator, occasioned by the earth's rotation,
being disregarded, because it is so small
as to produce no effect,) the spaces de-
scribed in the same1 time will retain the
same ratio ; now ms and OB being de-
scribed in the same time, and because
»IB : OB : : mn : OP, it follows that mn and
OP are also described in the same portion
of time, and therefore when the telescope
is in the situation nd the particle of light
will be at p in the telescope, and this
being the case in every moment of its
descent, the situation of the star, mea-
sured by the telescope at B, is 5, and the
angle ft BS is the aberration. Hence it
appears, that if we take BS : BR : : the
velocity of light: the velocity of the

m R

* This and some of the preceding definitions are given to illustrate
the 38th and 39th pages of White's Ephemeris, called Speculum Pha-

42 GEOGRAPHICAL THEOREMS. Part I

earth, and complete the parallelogram BRSS, the aberration will be
equal to the angle BSR or SBS ; s will be the true place of the star, and s
the 'place measured by the instrument, or its situation as seen by the
naked eye.

123. CENTRIPETAL FORCE is that force with which a
moving body is perpetually urged towards a centre, and
made to revolve in a curve instead of proceeding in a
straight line, for all motion is naturally rectilinear. — Cen-
tripetal force, attraction and gravitation, are terms of the
same import.

124. CENTRIFUGAL FORCE is that force with which a
body revolving about a centre, or about another body,
endeavours to recede from that centre, or body. — There
are two kinds of centrifugal force, viz. that which is given
to bodies moving round another body as a centre, usually
called the PROJECTILE FORCE, and that which bodies
acquire by revolving upon their own axes. Thus, for
example, the annual orbit of the earth round the sun is
described by the action of the centripetal and projectile
forces : — And the diurnal rotation of the earth on its
axis gives to all its parts a centrifugal force proportional
to its velocity.

Sir Isaac Newton has demonstrated, (Princiji. Prop. XIX. Booklll.)
that the " centrifugal force of bodies at the tr-uator, is to the centri-
" fugal force with which bodies recede from the earth, in the latitude
" of Paris, in the duplicate ratio of the radius to the co-sine qf the
" latitude. — And that the centripetal power in the latitude of Paris,
" is to the centrifugal force at the equator as 289 is to 1."

GEOGRAPHICAL THEOREMS.

1. THE latitude of any place is equal to the elevation
of the polar, star, (nearly) above the horizon ; and the
elevation of the equator above the horizon, is equal to
the complement of the latitude, or what the latitude
wants of 90 degrees.

nomenorum. The words elong. max. signify the greatest elongation of
a planet. InP/ate II. Fig. 2. E represents the earth, V Venus, and
S the sun. The elongation is the angle VES, measured by the arc

Chap. I. GEOGRAPHICAL THEOREMS. 43

2. All places lying under the equinoctial, or on the
equator, have no latitude, and all places situated on the
first meridian, have no longitude ; consequently that par-
ticular point on the globe where the first meridian inter-
sects the equator has neither latitude nor longitude.

3. The latitudes of places increase as their distances
from the equator increase. The greatest latitude a place
can have is 90 degrees.

4. The longitudes of places increase as their distances
from the first meridian increase, reckoned on the equator.
The greatest longitude a place can have is 180 degrees,
being half the circumference of the globe at that place ;
hence no two places can be at a greater distance from
each other than 180 degrees.

5. The sensible horizon varies as we travel from one
place to another, and its semi-diameter is affected by re-
fraction.

6. All countries upon the face of the earth, in respect
to time, equally enjoy the light of the sun, and are equally
deprived of the benefit of it ; that is, every inhabitant of
the earth has the sun above his horizon for six months,
and below his horizon for the same length of time.*

7. In all places of the earth, except exactly under the

* This, though nearly true, is not accurately so. The refraction in
high latitudes is very considerable, (see definition 85th), and near the
poles the sun will be seen for several days before he comes above the
horizon ; and he will, for the same reason, be seen for several days after
he has descended below the horizon. — The inhabitants of the poles (if
any) enjoy a very large degree of twilight, the sun being nearly two
months before he retreats 1 8 degrees below the horizon, or to the point
where his rays are first admitted into the atmosphere, and he is only two
months more before he arrives at the same parallel of latitude : and
particularly near the north-pole, the light of the moon is greatly in-
creased by the reflection of the snow, and the brightness of the Aurora
Borealis ; the sun is likewise about seven days longer in passing through
the northern than through the southern signs ; that is, from the vernal
equinox, which happens on the 21st of March, to the autumnal equinox,
which falls on the 23d of September, being the summer half-year to
the inhabitants of north latitude, is 1 86 days, the winter half-year is
therefore only 179 days. The inhabitants near the north-pole have
consequently more light in the course of a year than any other inha-
bitants on the surface of the globe.

44 GEOGRAPHICAL THEOREMS. Parti.

poles, the days and nights are of an equal length, (viz. 12
hours each,) when the sun has no declination, that is, on
the 21st of March, and on the 23d of September.

8. In all places situated on the equator, the days and
nights are always equal, notwithstanding the alteration of
the sun's decimation from north to south, or from south
to north.

9. In all places, except those upon the equator, or at
the two poles, the days and nights are never equal, but
when the sun. enters the signs of Aries and Libra, viz. on
the 21st of March, and on the 23d of September.

10. In all places lying under the same parallel of lati-
tude, the days and nights, at any particular time, are
always equal to each other.

11. The increase of the longest days from the equator
northward or southward, does not bear any certain ratio
to the increase of latitude ; if the longest days increase
equally, the latitudes increase unequally. This is evident
from the table of climates.

12. To all places in the torrid zone, the morning and
evening twilight are the shortest : to all places in the
frigid zones the longest ; and to all places in the tem-
perate zones, a medium between the other two.

13. To all places lying within the torrid zone, the sun
is vertical twice a year : to those under each tropic once,
but to those in the temperate and frigid zones, it is never
vertical.

14?. At all places in the frigid zones, the sun appears
every year without setting for a certain number of days,
and disappears for nearly the same length of time ; and
the nearer the place is to the pole, the longer the sun
continues without^ setting ; viz. the length of the longest
days and nights increase the nearer the place is to the
pole.

15. Between the end of the longest day and the
beginning of the longest night, in the frigid zone, and
between the end of the longest night, and the beginning
of the longest day, the sun rises and sets as at other
places on the earth.

16. At all places situated under the arctic or antarctic
circles, the sun when he has 23° 28' declination, appears

Chap. 1. GEOGRAPHICAL THEOREMS. 4s5

for 24 hours without setting ; but rises and sets at all
other times of the year.

17. At all places between the equator and the north-
pole the longest day and the shortest night are when the
sun has (23° 28') the greatest north decimation ; and the
shortest day and longest night are when the sun has
the greatest south declination.

18. At all places between the equator and the south-
pole the longest day and the shortest night are when the
sun has (23° 28') the greatest south declination ; and the
shortest day and longest night are when the sun has the
greatest north declination.

19. At all places situated on the equator the shadow
at noon of an object, placed perpendicular to the horizon,
falls towards the north for one half of the year, and
towards the south the other half.

20. The nearer any place is to the torrid zone, the
shorter the meridian shadow of an object will be. When
the sun's altitude is 45 degrees, the shadow of any per-
pendicular object is equal to its height.

21. The farther any place (situated in the temperate
or torrid zones) is from the equator, the greater the rising
and setting amplitude of the sun will be.

22. All places situated under the same meridian, so far
as the globe is enlightened, have noon at the same time.

23. If a ship set out from any port, arid sail round the
earth eastward to the same port again, the people in that
ship, in reckoning their time, will gain one complete day
at their return, or count one day more than those who
reside at the same port. If they sail westward they will
lose one day, or reckon one day less. To illustrate this,
suppose the person who travels westward should keep
pace with the sun, it is evident he would have continual
day, or it would be the same day to him during his tour
round the earth ; but the people who remained at the
place he departed from have had night in the same time,
consequently they reckon a day more than he does.

24. Hence, if two ships should set out at the same
time from any port, and sail round the globe, the one
eastward and the other westward, so as to meet at the
same port on any day whatever, they will differ two days

46 GEOGRAPHICAL THEOREMS. Part I.

in reckoning their time at their return. If they sail twice
round the earth they will differ four days; if thrice,
six, &c.

25. But if two ships should set out at the same time
from any port and sail round the globe, northward or
southward, so as to meet at the same port on any day
whatever, they will not diifer a minute in reckoning their
time, nor from those who reside at the port.

CHAPTER II.

Of the General Properties of Matter and the Laws of
Motion.

1. MATTER* is a substance which, by its different
modifications, becomes the object of our five senses ; viz.
whatever we can see, hear, feel, taste, or smell, must be
considered as matter, being the constituent parts of the
universe.

2. THE PROPERTIES OF MATTER are extension, figure,
solidity, motion, divisibility, gravity, and vis inertia.
These properties, which Sir Isaac Newton observes f are

* All substances when sufficiently heated ascend as invisible vapour,
or gas ; in other words, assume an aeriform state : hence it appears
that great heat would cause the whole material universe to vanish;
those bodies which we had previously considered the most solid becom-
ing as invisible and impalpable as the air we breathe. These consider-
ations have led some metaphysicians even to doubt the existence of
substance or matter, while those who admit its positive existence, yet
differ very essentially in defining this principle. The most minute
portion of any substance wliich the human eye, assisted with the most
powerful artificial aids, can perceive, is still a mass of many ultimate
particles or atoms, which will admit of being separated from each
other. Matter, therefore, may be defined, that inexplicable something
which is the foundation of all things, or from which all things that are
objects of our senses are formed, and is therefore distinguished from
body, which, though sometimes used synonymously, ought to be con-
fined to an extended solid substance possessing a definite form or
figure.

t Newton's Princip. Book III. — The third rule of reasoning in
philosophy.

Chap. II. GENERAL PROPERTIES OF MATTER. 47

the foundation of all philosophy, extend to the minutest
particles of matter.

3. EXTENSION, when considered as a property of
matter, has length, breadth, and thickness.

4. FIGURE is the boundary of extension ; for every
finite extension is terminated by, or comprehended under,
some figure.*

5. SOLIDITY is that property of matter by which it
fills space ; or by which any portion of matter excludes
every other portion from that space which it occupies*
This is sometimes defined the impenetrability of matter.

6. MOBILITY. Though matter of itself has no ability to
move ; yet as all bodies, upon which we can make suit-
able experiments, have a capacity of being transferred
from one place to another, we infer that motion is a
quality belonging to all matter. . •

7. DIVISIBILITY of matter signifies a capacity of being
separated into parts, either actually or mentally. That
matter is thus divisible, we are convinced by daily expe-
rience, but how far the division can be actually carried on
is not easily seen. The parts of a body may be so far
divided as not to be sensible to the sight; and by the
help of microscopes we discover myriads of organized
bodies totally unknown before such instruments were in-
vented. A grain of leaf gold will cover fifty square
inches of surface f, and contains two millions of visible
parts ; but the gold which covers the silver wire used .in
making gold lace is spread over a surface twelve times
as great. From such considerations as these, we are led
to conclude, that the division of matter is carried on to a
degree of minuteness far exceeding the bounds of our
faculties.

Mathematicians have shown that a line may be indefinitely divided
as follows: —

* Figure, as here defined, is the boundary of the whole body, or
extension ; but since figures thus considered frequently consist of
many sides or parts, these ought, perhaps, themselves to be defined.
Thus, the whole figure of a die, for instance, is composed of six sides,
or surfaces, which may be called the limits of the figure, and the edges
which separate these surfaces are lines, which last are, consequently,
the limits of the several surfaces of the figure or body. — ED.
t Adams's Natural and Experimental Philosophy. Lect. XXIV.

48 GENERAL PROPERTIES OF MATTER. Part I.

Draw any line AC, and another BM per-
pendicular to it, of an unlimited length to-
wards Q ; and from any point D, in AC, draw
DE, parallel to BM. Take any number of
points, r, o, N, M, in BQ; then from v as a
centre, and the distance PB, describe the arc

and in the same manner with o, N, M, as 4

centres, and distances OB, KB, and MB de-
scribe the arcs BO, Bn, BT». Now it is evi-
dent the farther the centre is taken from B,
the nearer the arcs will approach to D, and
the line ED will be divided into parts, each
smaller than the preceding one ; and since the line BM may be extended
to an indefinite distance beyond Q, the line ED may be indefinitely
diminished, yet it can never be reduced to nothing, because an arc of
a circle can never coincide with a straight line BC, hence it follows that
ED may be diminished ad infinitum*

8. GRAVITY* is that force by which a body endeavours
to descend towards the centre of the earth. By this
power of attraction in the earth, all bodies on every part
of its surface are prevented from leaving it altogether,
and people move round it in all directions, without any
danger of falling from it. — By the influence of attraction,
bodies, or the constituent parts of bodies, accede or have a
tendency to accede to each other, withoutany sensible mate-
rial impulse, and this principle is universally disseminated
through the universe, extending to every particle of matter.

9. INERTIA is that innate force of matter by which it
resists any change. We cannot move the least particle

* Gravity may be distinguished into particular and general, or ter-
restrial and universal. Particular, or terrestrial, gravity is that force
by which bodies are continually solicited towards a point which is
either accurately, or very nearly, the centre of the terraqueous globe,
and may be considered a familiar display of the energies of that pow-
erful but invisible agent in nature by the effect of which the planets
are retained in their orbits. General, or universal, gravity is that by
which all the great bodies of the solar system, and, indeed, all the
bodies and particles of matter in the universe, tend towards one
another ; or, in more appropriate terms, universal gravitation is that
effect of some unknown, but ever active and universal, cause, by which
every atom or particle of matter gravitates, or has a tendency towards
every other atom or particle. The law of gravitation sometimes, from
its universality, called the law of nature, may be thus expressed : —
" The mutual attraction between any two bodies is directly propor-
tional to their masses, or quantities of matter, and inversely to the
square of their distances from each other."— ED.

Chap. II. OF THE LAWS OF MOTION. 49

of matter without some exertion, and if one portion of matter
be added to another, the inertia of the whole is increased,
also if any part be removed the inertia is diminished. Hence,
the vis inertia of any body is proportional to its weight.

10. ABSOLUTE AND RELATIVE MOTION. A body is said
to be in absolute motion, when its situation is changed
with respect to some other body or bodies at rest; and to
be relatively in motion, when compared with other bodies
which are likewise in motion.

When a body always passes over equal parts of space
in equal successive portions of time, its motion is said to
be uniform.

When the successive portions of space described in equal
times continually increase, the motion is said to be acce-
lerated; and if the successive portions of space continually
decrease, the motion is said to be retarded. Also, the mo-
tion is said to be uniformly accelerated or retarded, when
the increments or decrements of the spaces, described in
equal successive portions of time, are always equal.

1 1. The VELOCITY of a body, or the rate of its motion, is
measured by the space uniformly described in a given time.

12. FORCE. Whatever changes, or tends to change, the
state of rest or motion of a body, is called force. If a
force act but for a moment, it is called the force of per-
cussion or impulse; if it act constantly, it is called an ac-
celerative force ; if constantly and equally, it is called an
uniform accelerative force.

GENERAL LAWS OF MOTION.

LAW I. " Every body perseveres in its state of rest, or uni-
" form motion in a straight line, unless it is compelled to
" change that state by forces impressed thereon." — New-
ton's Princip. Book I.*

Thus, when a body A is positively

at rest, if no external force put it in A@

motion, it will always continue at rest.

* This and the two following are generally termed Newton's three
Jaws of motion ; but that he was not the first inventor of them is evi-
dent, since they are in Des Cartels Principia Philosophies, Part II. pages
38, 39, and 40., which work was published before Newtoris Principia.

50 OF THE LAWS OF MOTION. Part I.

But if any impulse be given to it in the direction AB,
unless some obstacle, or new force, stop or retard its
motion, it will continue to move on uniformly, for ever,
in the same direction AB — Hence any projectile, as a ball
shot from a cannon, an arrow from a bow, a stone cast from
a sling, &c. would not deviate from its first direction, or
tend to the earth, but would continue in a straight line
with an uniform motion, if the action of gravity and the
resistance of the air did not alter and retard its motion.

LAW II. " The alteration of motion, or the motion gene-
" rated or destroyed, in any body, is proportional to the
" force applied ; and is made in the direction of that
" straight line in which the force acts." — Newton's Princip.
Book I.

Thus, if any motion be generated by a given force, a
double motion will be produced by a double force, a triple
motion by a triple force, &c. — and considering motion as
an effect, it will always be found that a body receives its
motion in the same direction with the cause that acts
upon it. — If the causes of motion be various, and in dif-
ferent directions, the body acted upon must take an
oblique or compound direction. Hence a curvilinear
motion cannot be produced by a simple cause, but must
arise from different causes,, acting at the same instant
upon the body.

LAW III. « To every action there is always opposed an
" equal re-action ; or the mutual actions of two bodies
" upon each other are always equal, and directed to con-
" trary points"— Newton's Princip. Book I.

If we endeavour to raise a weight by means of a lever,
we shall find the lever press the hands with the same
force which we exert upon it to raise the weight. Or if
we press one scale of a balance, in order to raise a
weight in the other scale, the pressure against the finger
will be equal to that force with which the other scale en-
deavours to descend.

When a cannpn is fired, the impelling force of the
powder acts equally on the breech of the cannon and on

Chap. 11. OF THE LAWS OF MOTION. 51

the ball, so that if the cannon, with its carriage, and the
ball were of equal weight, the carriage would recoil with
the same velocity as that with which the ball issues out
of the cannon. But the heavier any body is, the less will
its velocity be, provided the force which communicates
the motion continues the same. Therefore, so many
times as the cannon and carriage are heavier than the
ball, just so many times will the velocity of the cannon be
less than that of the ball.

COMPOUND MOTION.

1 . If two forces act at the same time on any body, and
in the same direction, the body will move quicker than it
would by being acted upon by only one of the forces.

2. If a body be acted upon by two equal forces, in exactly
opposite directions, it will not be moved from its situation.

3. If a body be acted upon by two unequal forces, in
exactly contrary directions, it will move in the direction of
the greater force.

4. If a body be acted upon by two forces, neither in the
same nor opposite directions, it will not follow either of the
forces, but move in a line between them.

The first three of the preceding articles may be con-
sidered as axioms, being self-evident ; the fourth may be
thus elucidated : Let a force be applied to a body at A,
in the direction AB, which would
cause it to move uniformly from
A to B in a given period of time ;
and, at the same instant, let an-
other force be applied in the di-
rection AC, such as would cause the body to move from
A to c in the same time which the first force would cause
it to move from A to B ; by the joint action of these forces,
the body will describe the diagonal AD of a parallelo-
gram * with an uniform motion, in the same time in

* A parallelogram is a four-sided figure, having its opposite sides
parallel, and consequently equal. EUCLID, 34 of I.
D 2

52 OF THE LAWS OF MOTION. Part I.

which it would describe one of the sides AB or AC by one
of the forces alone.

For, suppose a tube equal in length to AB (in which a
small ball can move freely from A to B) to be moved
parallel to itself from A to c, describing with its two ex-
tremities the lines AC and BD, so that the ball may move
in the tube from A to B in the same time that the tube
has descended to CD ; it is evident, that when the tube
AB coincides with the line CD, the ball will be at the ex-
tremity D of the line, and that it has arrived there in the
same time it would have described either of the sides AB
or AC. The ball will likewise describe the straight line

AD, for by assuming several similar parallelograms AEGF,
AKIH, &c. it will appear, that while the ball has moved
from A to E, the tube will have descended from A to F,
consequently the ball will be at G ; and while the ball has
moved from A to K, the tube will have descended from A
to H, and the ball will be at i. Now AGIO is a straight line ;
for smaller parallelograms that are similar to the whole,
and similarly situated, are about the same diagonal.*

5. If a body, by an uniform motion, describe one side of
a paralklogram, in the same time that it would describe the
adjacent side by an accelerative force ; this body, by tlie
joint action of these forces, would describe a curve, termi-
nating in the opposite angle of the parallelogram.

Let ABDC be a parallelogram, and suppose the body A
to be carried through AB by an uni-
form force in the same time that it
would be carried through AC by an
accelerative force, then by the joint
action of these forces, the body would
describe a curve AGIO. For, by the
preceding illustration, if the spaces

AE, EK, and KB, be proportional 'to each other, the spaces

AF, FH, and HC, will be in the same proportion, and the
line APID will be a straight line when the body is acted
upon by uniform forces ; But in this example, the force
in the direction AB being uniform, would cause the body

* EUCLID, 26 of VI.

Chap. II. OF THE LAWS OF MOTION.

to move over equal spaces AE, EK, and KB, in equal por-
tions of time ; while the accelerative force in the direc-
tion AC, would cause the body to describe spaces AF, FH,
and HC, increasing in magnitude in equal successive por-
tions of time, hence the parallelograms AEGF, AKIH, &c.
are not about the same diagonal *, therefore AGID is not
a straight line, but a curve.

6. The curvilinear motions of all the planets arise from
the uniform projectile forces of bodies in straight lines, and
the universal power of attraction which draws them off* from
these lines.

If the body E be pro-
jected along the straight
line EAF, in free space
where it meets with no re-
sistance, and is not drawn
aside by any other force,
it will (by the first law of
motion) go on for ever in
the same direction, and
with the same velocity.
For, the force which
moves it from E to A in a
given time will carry it from A to F in a successive and
equal portion of time, and so on; there being nothing
either to obstruct or alter its motion. But if, When the
projectile force lias carried the body to A, another body,
as s, begins to attract it, with a power duly adjusted and
perpendicular to its motion at A, it will be drawn from
the straight line SAP, and revolve about s in the circle t
A GOO A. When the body E arrives at o, or any other
part of its orbit, if the small body M, within the sphere of
E'S attraction, be projected, as in the straight line M »,
with a force perpendicular to the attraction of E, it will
go round the body E, in the orbit m, and accompany E in

* EUCLID, 24 of VI.

t If any body revolve round another in a circle, the revolving body
must be projected with a velocity equal to that which it would have
acquired by falling through half the radius of the circle towards the
attracting body. Emerson s Cent. Forces, Prop. ii.
D 3

54? OF THE LAWS OF MOTION. Parti.

its whole course round the body s. — Here s may repre-
sent the sun, E the earth, and M the moon.

If the earth at A be attracted towards the sun at s, so
as to fall from A to H by the force of gravity alone, in the
same time which the projectile force singly would have
carried it from A to F ; by the combined action of these
forces it will describe the curve AG ; and if the velocity
with which E is projected from A, be such as it would
have acquired by falling from A to v (the half of AS) by
the force of gravity alone *, it will revolve round s in a
circle.

* A body, by the force of gravity alone, falls 16-j^feet in the first
second of time, and acquires a velocity which will carry it uniformly
through 32£ feet in each succeeding second. This is proved experi-
mentally by writers on mechanics.

[The pupil should be carefully guarded against confounding the
law alluded to in the above note as regulating the descent of falling
bodies, and which is properly the law of terrestrial gravitation, with the
law of universal gravitation explained in note *, page 48. To prevent
ambiguity, it may be necessary to explain the subject (being an im-
portant one) a little more at length. The law by which universal
gravitation acts is that it decreases as the squares of the distances from
the body towards which the gravitation is made increase: a body,
therefore, near the surface of the earth, tends towards the centre with
four times the force that it would do if it were removed twice as far
from that centre ; nine times the force that it would do at thrice the
distance, and so on : but the distances to which we can have access,
either above or below the earth's surface, are so small that it is scarcely
possible by any direct experiment upon the weight of a body to detect
any sensible change in the force of gravity itself. We may, therefore,
in all our reasonings concerning the effects it produces near the
earth's surface consider it a constant force, and ascribe the increase of
velocity in a falling body not to the attraction of the earth acting
more strongly upon it as it approaches the earth's surface, but to the
continuance of this force. Thus every body actually falls in vacuo
1 6T'5 feet during the first second of its descent in the latitude of London,
at the end of which time it has acquired such an increase of velocity as
would carry it through double that space, or 32£ feet in the next
second of time, if the force of gravity were to cease acting upon it ;
but the velocity continuing to increase by the power of gravity conti-
nuing to act upon the body, it actually in this second passes over
three times as much space as it passed over in the first second: this
added to one makes four. In the third second, five times the space,
which added to the four makes nine, and so on, always increasing by
the odd numbers : hence we obtain for the descent of circumterrestrial

Chap. II. OF THE LAWS OF MOTION.

7. If one body revolve round another (as the earth round
the sun), so as to vary its distance from the centre of mo-
tion, the projectile and centripetal forces must each be varia-
ble, and the path of the revolving body will differ from a
circle.

Thus, if while a
projectile force would
carry a planet from A
to F, the sun's attrac-
tion at s would bring c
it from A to H, the gra-
vitating power would
be too great for the
projectile force; the
planet, therefore, in-
stead of proceeding
in the circle ABC (as
in the preceding ar-
ticle) would describe
the curve AO, and ap-
proach nearer to the
sun ; so, being less
than SA. Now, as the centripetal force, or gravitating
power, always increases as the square of the planet's dis-
tance from the sun diminishes*, when the planet arrives
at o the centripetal force will be increased, which will
likewise increase the velocity of the planet, and accelerate
its motion from o to v ; so as to cause it to describe the
arcs OP, PQ, QR, RD, DT, TV, successively increasing
in magnitude, in equal portions of time. The motion of
the planet being thus accelerated, it gains such a centri-
fugal force, or tendency to fly off at v, in the line vw, as

bodies this simple rule — the spaces passed over are directly as the
square of the times. Now, as in the first second of time, a body falls
through vl 6-^ feet, in order to find the space a body passes through in
its descent, we have only to square the seconds, and multiply the pro-
duct by IG-jL feet. To the power of gravity, therefore, considered as
a constant force, we are to ascribe the descent of a projectile in a
curved line. — ED.]

* Newton's Princip. Book ill. Prop. II.
D 4-

55 OF THE LAWS OF MOTION. Parti.

overcomes the sun's attraction ; this centrifugal or projec-
tile force being too great to allow the planet to approach
nearer the sun than it is at v, or even to move round the
sun in the circle tabcd, &c. it flies off in the curve
XZMA, with a velocity decreasing as gradually from v to
A, as if it had returned through the arcs VT, TD, DR,
&c., to A, with the same velocity which it passed through
these arcs in its motion from A, towards v. At A the
planet will have acquired the same velocity as it had at
first, and thu$ by the centrifugal and centripetal forces it
will continue to move round s.

Two very natural questions may here be asked ; viz.
why the action of gravity, if it be too great for the pro-
jectile force at o, does not draw the planet to the sun
at s? and why the projectile force at v, if it be too
great for the centripetal force, or gravity, at the same
point, does not carry the planet farther and farther from
the sun, till it is beyond the power of his attraction ?

First. If the projectile force at A were such as to carry
the planet from A to G, double the distance, in the same
time that it was carried from A to F, it would require
four* times as much gravity to retain it in its orbit, viz.
it must fall through AI in the time that the projectile
force would carry it from A to G, otherwise it would not
describe the curve AOP. But an increase of gravity gives
the planet an increase of velocity, and an increase of
velocity increases the projectile force ; therefore, the
tendency of the planet to fly off from the curve in a tan-
gent P m, is greater at P than at o, and greater at Q than
at P, and so on ; hence, while the gravitating power in-
creases, the projectile power increases, so that the planet
cannot be drawn to the sun. •

Secondly. The projectile, force is the greatest at, or
near, the point v, and the gravitating power is likewise
the greatest at that point. For if AS be double of vs,
the centripetal force at v will be four times as great as
at A, being as the square of the distance from the sun.
If the projectile force at v be double of what it was

Ferguson's Astronomy, Art. 153.

Chap. III. OF THE FIGURE OF THE EARTH, &C. 57

at A, the space vw, which is the double of AF, will be
described in the same time that AF was described, and
the planet will be at x in that time. Now, if the action
of gravity had been an exact counterbalance for the'
projectile force during the time mentioned, the planet
would have been at t, instead of x, and it would describe
the circle t, a, b, c. &c. ; but the projectile force being
too powerful for the centripetal force, the planet recedes
from the sun at s, and ascends in the curve XZM, &c.
Yet, it cannot fly off in a tangent in its ascent, because
its velocity is retarded, and consequently its projectile
force is diminished, by the action of gravity. Thus,
when the planet arrives at z, its tendency to fly off in a
tangent zrc, is just as much retarded, by the action of
gravity, as its motion was accelerated thereby at Q, there-
fore it must be retained in its orbit.

CHAPTER III.
Of the Figure of the Earth, and its Magnitude.

THE figure of the earth, as composed of land and water,
is nearly spherical ; the proof of this assertion will be
the principal object of this chapter. The ancients held
various opinions respecting the figure of the earth ; some
imagined it to be cylindrical, or in the form of a drum ;
but the general opinion was that it was a vast extended
plane, and that the horizon was the utmost limit of the
earth, and the ocean the bound of the horizon. These
opinions were held in the infancy of astronomy ; and, in
the early ages of Christianity, some of the fathers went
so far as to pronounce it heretical for any person to
declare that there was such a thing as the antipodes.
But by the industry of succeeding ages, when astronomy
and navigation were brought to a tolerable degree of
perfection, and when it was observed that the moon was
frequently eclipsed by the shadow of the earth, and that
such shadow always appeared circular on the disc or face
of the moon, in whatever position the shadow was pro-
D 5

58 OF THE FIGURE OF THE EARTH, &C. Part I.

jected, it necessarily followed that the earth, which cast
the shadow, must be spherical ; since nothing but a
sphere, when turned in every position with respect to
a luminous body, can cast a circular shadow ; likewise all
calculations of eclipses, and of the places of the planets,
are made upon supposition that the earth is a sphere,
and they all answer to the true times, when accurately
calculated. When an eclipse of the moon happens, it is
observed sooner by those who live eastward than by
those who live westward; and, by frequent experience,
astronomers have determined that, for every fifteen
degrees difference of longitude, an eclipse begins so
many hours sooner in the easternmost place, or later
in the westernmost. If the earth were a plane, eclipses
would happen at the same time in all places, nor could
one part of the world be deprived of the light of the sun
while another part enjoyed the benefit of it. The
voyages of the circumnavigators sufficiently prove that
the earth is round from west to east. The first who at-
tempted to circumnavigate the globe was Magellan, a
Portuguese, who sailed from Seville in Spain on the 10th
of August 1519; he did not live to return, but his ship
arrived at St. Lucar, near Seville, on the 7th of Sep-
tember 1522, without altering its direction, except to
the north or south, as compelled by the winds or inter-
vening land. Since this period, the circumnavigation of
the globe has been performed at different times by Sir
Francis Drake, Lord Anson, Captain Cook, &c. The
voyages of the circumnavigators have been frequently
adduced by writers on geography and the globes, to
prove that the earth is a sphere ; but when we reflect
that all the circumnavigators sailed westward round the
globe (and not northward and southward round it), they
might have performed the same voyages had the earth
been in the form of a drum or cylinder ; but the earth
cannot be in the form of a cylinder, for if it were, then
the difference of longitude between any two places
would be equal to the meridional distance between the
same places, as on a Mercator's chart, which is contrary
to observation — Again, if a ship sail in any part of the
world, and upon any course whatever, on her departure

Chap. III. OF THE FIGURE OF THE EARTH, &C. 59

from the coast, all high towers or mountains gradually
disappear, and persons on shore may see the masts of the
ship after the hull is hidden by the convexity of the water
(see Figure III. Plate 1.} — If a vessel sail northward, in
north latitude, the people on board may observe the polar
star gradually to increase in altitude the farther they go ;
they may likewise observe new stars continually emerging
above the horizon, which were before imperceptible ; and
at the same time those stars which appear southward will
continue to diminish in altitude till they become invisible.
The contrary phenomena will happen if the vessel sail
southward ; hence the earth is spherical from north to
south, and it has already been shewn that it is spherical
from east to west.

The arguments already adduced clearly prove the
rotundity of the earth, though common experience shews
us that it is not strictly a geometrical sphere ; for its sur-
face is diversified with mountains and valleys : but these
irregularities no more hinder the earth from being reckoned
spherical, considering its magnitude, than the roughness
of an orange hinders it from being esteemed round.*

When philosophical and mathematical knowledge ar-
rived at a still greater degree of perfection, there seemed
to be a very sufficient reason for the philosophers of the
last age to consider the earth not truly spherical, but
rather in the form of a spheroid, f This notion first arose

* Our largest globes are in general 1 8 inches in diameter. The
diameter of the earth is about 7964 miles. Chimborazo, one of the
highest of the Andes mountains, is about 21,440 feet, or about four
miles high. The radius of the earth is 3982 miles, and that of an
18-inch globe 9 inches. Now by the rule of three, 3982m : 3982 m
+ 4 :: 9 in. : 9-009, from which deduct the radius of the artificial
globe, the remainder -009 = ^ = ^ of an inch, nearly, is the ele-
vation of the Andes on an 18-inch globe, which is less than a grain
of sand. One of the highest points of the Himalaya mountains to
the north of Hindoostan surveyed by Capt. Blake, and deduced from
his observations by Mr. Colebrooke, is 28,015 feet above the level of
the sea. Edinburgh Philosophical Journal, vol. v. p. 408.

f A spheroid is a figure formed by the revolution of an ellipsis about

its axis, and an ellipsis is a curve-lined figure in geometry, formed by

cutting a cone or cylinder obliquely ; but its nature will be more

clearly comprehended, by the learner, from the following description.

D 6

60 OF THE FIGURE OF THE EART*H, &C. Part 1.

from observations on pendulum clocks*, which being
fitted to beat seconds in the latitudes of Paris and Lon-
don, were found to move slower as they approached the
equator, and at, or near, the equator, they were obliged
to be shortened about £ of an inch to agree with the times
of the stars passing the meridian. This difference appear-
ing to Huygensf and Sir Isaac Newton, to be a much
greater quantity than could arise from the alteration by
heat only, they separately discovered that the earth was
flatted at the poles. J — By the revolution of the earth
on its axis (admitting it to be a sphere) the centrifugal force

Let TR (in Plate IV. Figure V.) be the transverse diameter, or
longer axis of the ellipsis, and co the conjugate diameter, or shorter
axis. With the distance TD or DR in your compasses, and c as a centre,
describe the arc rf : the points F, f, will be the two foci of the ellipsis.
Take a thread of the length of the transverse axis TR, and fasten its
ends with pins in F and f, then stretch the thread Fif, and it will reach
to i in the curve, then by moving a pencil ro.und with the thread, and
keeping it always stretched, it will trace out the ellipsis TCRO. — If
this ellipsis be made to revolve on its longer axis TR, it will generate
an oblong spheroid, or Cassinis figure of the earth ; but if it be sup-
posed to revolve on its shorter axis co, it will form an oblate sjiheroid,
or Sir Isaac Newton's figure of the earth. — The orbits or paths of
all the planets are ellipses, and the sun is situated in one of theybci
of the earth's orbit, as will be observed farther on. — The points F, f,
are called foci, or burning points ; because if a ray of light issuing
from the point F meet the curve in the point i, it will be reflected back
into the focus f. For lines drawn from the two foci of an ellipsis to
any point in the curve, make equal angles with a tangent to the curve
at that point ; and by the laws of optics the angle of incidence is equal
to the angle of reflection. Robertson's Conic Sections, Book III.
Scholium to Prop. ix.

* Philosophical Transactions, No. 386.

t A celebrated mathematician born at the Hague in Holland, in 1 629.

| The length of a pendulum at the equator, is to the length of a
pendulum at the pole, as the axis of the earth is to the equatorial
diameter. Emerson's Math. Geog. Prop. XI. M. Laplace (Expo-
sition du Systeme du Monde) has shewn, that if the force of gravity at
the equator be represented by 1, at the poles it will be 1 -00567 ; and at
the intermediate latitudes of 30°, 45°, 52°, and 60° ; it will be 1-00141,
1-00283, 1-00357, and 1-00423 respectively, and these numbers
will represent the ratios between the lengths of pendulums vibrating
seconds in these different latitudes. The length of a pendulum at the
equator is 39-06 inches, at the poles 39-281, and in latitudes 30°, 45°,
52°, and 63°, the respective lengths are 39'1 1 5, 39-1 7, 39*2, and 39-225.

Chap. III. OF THE FIGURE OF THE EARTH, &C. 61

at the equator would be greater than the centrifugal force
in the latitude of London or Paris, because a larger circle
is described by the equator, in the same time : but as the
centrifugal force (or tendency which a body has to re-
cede from the centre) increases, the action of gravity
necessarily diminishes : and where the action of gravity is
less, the vibrations of pendulums of equal lengths become
slower : hence, supposing the earth to be a sphere, we
have two causes why a pendulum should move slower at
the equator than at London or Paris, viz. the action of
heat which dilates all metals, and the diminution of gra-
vity. But these two causes combined would not, accord-
ing to Sir Isaac Newton, produce so great a difference as
|th of an inch in the length of a pendulum, he therefore
supposed the earth to assume the same figure that a ho-
mogeneous fluid would acquire by revolving on an axis,
viz. the figure of an oblate spheroid, and found that the
" diameter of the earth at the equator, is to its diameter
from pole to pole, as 230 to 229."* Notwithstanding
the deductions of Sir Isaac Newton, on the strictest ma-
thematical principles, many of the philosophers in France,
the principal of whom was Cassini-j*, asserted that the
earth was an oblong spheroid, the polar diameter being
the longer ; and as these different opinions were supposed

* Motte's translation of Newton's Principia, Book III. page 243.
Calling the equatorial diameter of the earth 7964 English miles, the
polar diameter will be 7929. — For 230 : 229 : : 7964 : 7929 miles,
the polar axis. Hence the polar axis is shorter than the equatorial
diameter by 35 miles, and the earth is higher at the equator than at the.
poles by 17?,- miles, a difference imperceptible on the largest globes that
are made. — Suppose a globe to be 1 8 inches in diameter at the equator,
then 230 ; 229 :: 18 : 17 |jf, the polar diameter : the difference of the
diameters is ^ of an inch, half difference is 5§jj of an inch, the flat-
ness of an 18-inch globe at each pole, which is less than the 23rd part
of an inch, or not much thicker than the paper and paste, a quantity
not to be discovered by the appearance ; and on smaller globes the dif-
ference would be considerably less. Hence the learner should be
informed, that though the earth be not strictly a globe, it cannot be
represented by any other figure which will give so exact an idea of its
shape ; and a lecturer who informs his hearers that it is in the shape of
a turnip or an orange, gives a very false idea of its true figure.

f Son of the celebrated Italian astronomer ; he was born at Paris
in 1677.

62 OF THE FIGURE OF THE EARTH, &C. Parti.

to retard the general progress of science in France, the
king resolved that the affair should be determined by
actual admeasurement at his own expense. Accordingly,
about the year 1735, two companies of the most able ma-
thematicians of that nation were appointed : the one to
measure the degree of a meridian as near to the equator
as possible, and the other company to perform a like
operation as near the pole as could be conveniently
attempted. The results of these admeasurements con-
tradicted the assertions of Cassini, and of J. Bernoulli
(a celebrated mathematician of Basil in Switzerland, who
warmly espoused his cause), and confirmed the calcula-
tions of Sir Isaac Newton — In the year 1756, the Royal
Academy of Sciences of Paris appointed eight astrono-
mers to measure the length of a degree between Paris
and Amiens ; the result of their admeasurement gave
57069 toises for the length of a degree.

The utility of finding the length of a degree in order
to determine the magnitude and figure of the earth, may
be rendered familiar to a learner thus : suppose I find the
latitude of London to be 51£° north, and travel due north
till I lind the latitude of a place to be 52-J° north, I shall
then have travelled a degree, and the distance between
the two places, accurately measured, will be the length
of a degree ; now if the earth be a correct sphere, the
length of a degree on a meridian, or a great circle, will
be equal all over the world, after proper allowances are
made for elevated ground, &c. ; the length of a degree
multiplied by 360 will give the circumference of the
earth, and hence its diameter, &c. will be easily found ;
but if the earth be any other figure than that of a sphere,
the length of a degree on the same meridian will be
different in different latitudes, and if the figure of the
earth resemble an oblate spheroid, the lengths of a degree
will increase as the latitudes increase. The English trans-
lation of Maupertuis's figure of the earth concludes with
these words : (see page 163 of the work) « The degree of
" the meridian which cuts the polar circle being longer
" than a degree of the meridian in France, the earth is a
« spheroid flatted towards the poles." For, the longer
a degree is, the greater must be the circle of which it is

Chap. III. OF THE FIGURE OF THE EARTH, &C. 63

a part ; and the greater the circle is, the less is its curva-
ture.

The first person who measured the length of a degree
with any appearance of accuracy was Mr. Richard Nor-
wood: by measuring the distance between London and
York he found the length of a degree to be 367196 English
feet, or 69£ English miles ; hence, supposing the earth to
be a sphere, its circumference will be 25020 miles, and
its diameter 7964? * miles ; but if the length of a degree,
at a medium, be 57069 toises, the circumference of the
earth will be 24873 English miles, its diameter 7917 miles,
and the length of a degree 69^ miles, f

CONCLUSION. Notwithstanding all the admeasurements
that have hitherto been made, it has never been demon-
strated, in a satisfactory manner, that the earth is strictly

* 5280 feet make a mile, therefore 367196 divided by 5280 gives
69£ miles nearly, which multiplied by 360 produces 25020 miles, the
circumference of the earth ; but the circumference of a circle is to its
diameter as 22 to 7, or more nearly as 355 to 113; hence 355 : 113
: : 25020 miles : 7964 miles, the diameter of the earth. Again, 6
French feet make 1 toise, therefore 57069 toises are equal to 342414
French feet ; but 107 French feet are equal to 114 English feet, hence
107 F. f. : 114E. f. : : 342414 F. f. : 364814 English feet, which di-
vided by 5280, the feet in a mile, gives 69.09 miles, the length of a
degree by the French admeasurement. Or, 342414 multiplied by 360
produces 123269040 French feet, the circumference of the earth, and
107 : 114 : : 12326904O : 131333369 English feet, equal to 24873.74
miles, the circumference of the earth, and 355 : 113 : : 24873.74 :
7917 miles, the diameter of the earth.

f The length of a degree in lat. 51° 9' N. is 364950 feet = 69.12
English miles. Trigonometrical Survey of England and Wales,
Vol. II. Part II. page 113. Mr. Swanberg, a Swedish mathemati-
cian, found tne length of a degree to be 57 196. 159 toises = 365627.782
English feet = 69.247 miles.

[According to La Place, the celebrated French astronomer, the
earth's equatorial diameter is 7924 miles; and Sir J. F. W. Herschel
(See Cab. Cyc. ASTRONOMY) gives the following dimensions, which
appear to be the most accurate of any that have yet been published:—

Feet Miles.

Greater or equatorial diameter - - 41,847,426 = 7925.648

Lesser or polar diameter - - - 41,707,620 = 7899.170

Difference of diameters or polar compres-
sion - - 139,806 = 26.478
Hence the proportion of the diameters is very nearly that of 298 : 299,
and their difference ^5 of the greater, or a very little more than id*. —
EDITOR.]

64- OF THE DIURNAL AND ANNUAL Part I.

a spheroid ; indeed, from observations made in different
parts of the earth, it appears that its figure is by no
means that of a regular spheroid, nor that of any other
known regular mathematical figure, and the only certain
conclusion that can be drawn from the works of the seve-
ral gentlemen employed to measure the earth, is, that
tJie earth is something more flat at the poles than at the
equator. — The course of a ship, considering the earth a
spheroid, is so near to what it would be on a sphere, that
the mariner may safely trust to the rules of globular sail-
ing*, even though his course and distance were much
more certain than it is possible for them to be. For which,
and similar reasons, mathematicians content themselves
with considering the earth as a sphere in all practical
sciences, and hence the artificial globes are made perfectly
spherical, as the best representation of the figure of the
earth.

CHAPTER IV.
Of the Diurnal and Annual Motion of the Earth.

THE motion of the earth was denied in the early ages
of the world, yet as soon as astronomical knowledge be-
gan to be more attended to, its motion received the assent
of the learned, and of such as dared to think differently
from the multitude, or were not apprehensive of ecclesi-
astical censure. — The astronomers of the last and present
age have produced such a variety of strong and forcible
arguments in favour of the motion of the earth, as must
effectually gain the assent of every impartial inquirer. —
Among the many reasons for the motion of the earth, it
will be sufficient to point out the following :

1. Of the Diurnal Motion of the Earth.
The earth is a globe of 7912 miles in diameter, and by

* Robertson's Navigation, Book VIII. Art. 143.

Chap. IV. MOTION OF THE EARTH. 65

revolving on its axis every 24 * hours from west to east, it
causes an apparent diurnal motion of all the heavenly
bodies from east to west — We need only look at the sun,
or stars, to be convinced, that either the earth, which is
no more than a point f when compared with the heavens,
revolves on its axis in a certain time, or else the sun,
stars, &c. revolve round the earth in nearly the same
time. Let us suppose, for instance, that the sun revolves
round the earth in 24 hours, and that the earth has no
diurnal motion. — Now, it is a known principle in the laws
of motion, that if any body revolve round another as its
centre, it is necessary that the central body be always in
the plane in which the revolving body moves, whatever
curve it describes $ ; therefore if the sun move round the
earth in a day, its diurnal path must always describe a
circle which will divide the earth into two equal hemi-
spheres. But this never happens except on two days of
the year, viz. at the time of the equinoxes, when the sun
rises exactly in the east, and sets exactly in the west.
For, from the 21st of March to the 23d of September the
sun rises to the north of the east, and sets to the north of
the west ; and from the 23d of September to the 21st of
March, it rises to the south of the east, and sets to the
south of the west, and therefore its diurnal path divides
the globe into two unequal parts.

The fixed stars also (except those which lie in the equi-
noctial) do not appear to revolve round the centre of the
earth, but its axis, in circles parallel to its equator, and
diminishing in magnitude from the equinoctial to the
poles ; affording another very satisfactory argument in
favour of the earth's rotation. If, moreover, the earth be
considered immovable, the sun, whose distance from it is
95,000,000 miles, in order to complete his revolution in
24 hours, must travel at the rate of 400,000 miles per
minute ; and the stars, from their immeasurable distance,

* That is, the time from the sun's being on the meridian of any
place, to the time of its returning to the same meridian the next day;
but the earth performs a complete revolution on its axis in 23 hours
56 minutes 4-09 seconds; see definition 61. page 14.

f Dr. Keill, Lect. 26.

j Emerson's Astronomy, p. 11

66 OF THE DIURNAL AND ANNUAL Part I.

must revolve millions of millions more rapidly than the
sun. It is also well known that the sun is above a million
times larger than the earth, and it is highly probable that
each of the stars is at least equal to it in magnitude : yet,
if we do not admit the rotation of the earth, an infinite
number of these prodigious bodies must be supposed to be
perpetually circulating about our comparatively insignifi-
cant globe, not only with degrees of velocity far surpass-
ing human conception, but exactly adapted to the
respective distances of each of these individual bodies ;
thus introducing a complication of motion no less surprising
than the prodigious velocity with which it is performed,
all which improbabilities are got rid of by the simple
hypothesis of the earth's revolution on its axis.

It is no argument against the earth's diurnal motion
that we do not feel it ; a person in the cabin of a ship, on
smooth water, cannot perceive the ship's motion when
it turns gently and uniformly round* ; neither does the
motion of the -earth cause bodies to fall from its surface ,
for all bodies, of whatever matter they are composed, are
drawn to the earth by the power of its central attractionf,
which, laying hold of them according to their densities,
or quantities of matter, without regard to their magni-
tudes, constitutes what we call weight.

The phenomena of the apparent diurnal motion of the
sun may be explained by the motion of the earth ; thus,
let IFGH (Plate I. Fig. V.) represent the earth, s the sun,
and the circle DSBC the apparent concavity of the hea-
vens. Let the earth revolve on its axis from i towards F
(viz. from west to east). Suppose a spectator to be at I,
the sun, which is at an immense distance, and enlightens
half the globe at once, will appear to be rising. As the
earth moves round, the spectator is carried towards F, and
the sun seems to increase in height ; when he has arrived
at F, the sun is at the highest. As the earth continues to
turn round, the spectator is carried from F towards G, and
the altitude of the sun keeps continually diminishing ;
when he has arrived at G, the sun is setting. During the
time the spectator has been carried from i to G, the sun

' Ferguson's Astronomy. Art. 119.
f Newton's Principia, Book III. Prop. vii.

Chap. IV. MOTION OF THE EARTH. 67

has appeared to move the contrary way. Hence it is evi-
dent that while the spectator is carried through the illu-
minated half of the earth, it is day-light ; at the middle
point F, it is noon ; also while he is carried through the
dark hemisphere, it is night; and at H it is midnight.
Thus the vicissitude of day and night evidently appears by
the rotation of the earth about its axis : what has been
said of the sun is equally applicable to the moon, or any
star placed at s ; therefore all the celestial bodies seem to
rise and set by turns, according to their various situations.
The spectator at i, F, G, H, will always have his feet
towards the centre of the earth, and the sky above his
head, whatever position the earth may have ; agreeably to
the laws of gravitation or attraction. Thus an inhabitant
at a will be the most powerfully attracted towards his an-
tipodes b, because there is the greatest mass of earth under
his feet in that direction ; for the same reason b will be
the most attracted towards a, m towards n, and n towards
m, &c. ; hence it appears that every body on the surface
of the earth is attracted towards its centre, or rather
towards the antipodes of that body, for the whole earth is
the attracting mass, and not some unknown substance
placed in the centre of the earth.

2. Of the Annual Motion of the Earth.
The diurnal revolution of the earth on its axis being
proved, the annual motion round the sun will be- readily
admitted ; for, either the earth moves round the sun in a
year, or else the sun moves round the earth : now, by the
laws of centripetal force, if two bodies revolve about each
other, they revolve round their common centre of gra-
vity *; and it is evident, that if the two bodies be of equal
magnitude and density, the centre of gravity will be equi-
distant from each body ; but, if they be of different mag-
nitudes, the centre of "gravity will be nearest to the larger
body : if the earth, therefore, remain in the same situation
while the sun revolves round it, its magnitude must be
much greater than that of the sun ; for it is contrary

* The centre of gravity of two bodies is a certain point in a line
supposed to join their centres; which point being supported, the two
bodies would likewise be supported, and rest in equilibrium.

68 OF THE DIURNAL AND ANNUAL Part I.

to the laws of nature for a heavy body to revolve round a
light one as its centre of motion : but from observations
on the dimensions * and distances of the sun and planets,
it appears that the sun so greatly exceeds, not only the
earth, but the planets, in magnitude, that the common
centre of gravity of the whole is almost constantly within
the body of the sun, so that the sun's motion round the
common centre of gravity of the earth and the planets is
not perceptible by ordinary observers. Not only the
earth, therefore, but the planets, move round the sun.

It is also evident that the motion of the earth in its
orbit is from west to east, for if the sun be observed to
rise with any fixed star which is near the ecliptic, it will,
in the course of a few days, appear to the eastward of
that star. And in the period of a year it will arrive at the
same star again.

The earth is computed to be 95 millions of miles from
the sun -j-, and performs its revolution round him, de-

* The apparent diameters of the planets are found by a micrometer
placed in the focus of a telescope, or, the apparent diameter of the sun
may be measured by means of the projection of his image into a dark
room, through a circular aperture. From these apparent diameters,
and the respective distances from the earth, the real diameters of the
sun and planets may be determined.

f In Plate IV. Fig. vi. let o be the centre of the earth, p the place
of an observer on its surface, and s the sun or a planet in the heavens :
now to an observer at o, the sun would appear at a, and to an observer
at p it would appear at b ; the arc a, b, or the angle a s b, which is
equal to the angle PSO, is called the horizontal parallax. Mr. Short,
in vol. 52. part ii. of the Philosophical Transactions, has determined
the horizontal parallax of the sun to be 8'' -65, at its mean distance
from the earth. Hence, by trigonometry,

Logarithmical sine of 8'' -65, or angle PSO - - 5-621914O
Is to one semi-diameter of the earth PO - - - 0-0000000
As radius, sine of 90 degrees, or sign of OPS - 10-0000000
Is to 23882-84 semi-diameters - - - - _ 4-3780860

Now if we take the diameter of the earth 7970 miles, as Mr. Short
has done, the semi-diameter 3985 multiplied by 23882-84 gives
951731 17 miles, the distance of the earth from the sun : if the diameter
of the. earth be taken 7964 miles, the distance will be 95101468
miles ; if it be taken 7917 miles, (see the chapter of the Figure of the
Earth), the distance will be 94540222 miles. In a case of such uncer-

Chap. IV. MOTION OF THE EARTH. 69

scribing an elliptical orbit or path*, in 365 days 5 hours
48 minutes and 49 seconds, from any equinox or solstice
to the same again ; it travels at the rate of upwards of
68,000 miles per hour.t Besides this motion, which is
common to every inhabitant of the earth, the inhabitants
at the equator are carried 1036'5 J miles every hour by the
diurnal revolution of the earth on its axis, while those in
the parallel of London are carried only about 644 miles
per hour. The axis of the earth makes an angle of 23°
28' with a perpendicular to the plane of its orbit, and
keeps always the same oblique direction throughout its
annual course { ; hence it follows, that, during one part
of its course, the north pole is turned towards the sun,
and, during another part of its course, the south pole is
turned towards it in the same proportion ; which is the
cause of the different seasons, as spring, summer, autumn,

tainty, where a very small error in the parallax will produce an
astonishing difference in the conclusion of the process, and where an
error in the diameter of the earth will also affect the operation, we
may rest content with estimating the distance of the earth from the
sun at 95 millions of miles. Mr. WoodJiouse, in his Astronomy,
page 384, calculates the sun's horizontal parallax to be 8" -701 7, and
at page 284» where he has given the distances of the planets from the
sun according to Laplace, he states the distance of the earth from the
sun to be 93726900 miles.

* The idea that the earth moved in an elliptical orbit was first con-
ceived by Kepler, an eminent German astronomer, and demonstrated
by Sir Isaac Newton. Seethe Principia, Book III. Prop. xiii.

•f* The earth's distance from the sun is 95 millions of miles, the
mean diameter of its orbh>is therefore 190 millions of miles, and the
circumference of a circle is three times the diameter and one seventh
more; or the circumference is to the diameter as 355 to 113 more
nearly; hence 113 : 355 : : 1900OOOOO -.596902654, the circumfer-
ence of the orbit ; but this circumference is described in 365 days 5
hours 48 minutes 49 seconds, or 365 days 6 hours nearly, or 8766
hours ; hence 8766 h. : 596902654 m. : : 1 h. : 68092 miles per hour
the inhabitants of the earth are carried by its annual revolution.

\ These distances are found by multiplying the number of miles
contained in a degree in any parallel of latitude by 15 ; thus, the cir-
cumference of the earth at the equator is 360 x 69^ m., and in the
latitude of London it is equal to 360x42-95, and 24 h. : 360° x
69-1 : : 1 h. : 1036'5m. ; or 1 : 15 x 69'1 : : 1 : 1036'5m.

§ This is not strictly true, though the variation, called the nutation
of the earth's axis, is scarcely perceptible in two or three years.

70 OF THE DIURNAL AND ANNUAL Part I.

and winter. The orbit of the earth being elliptical, the
earth must at some times approach nearer to the sun
than at others, and will of course take more time in
moving through one part of its path than through another.
Astronomers have observed that the motion of the earth
is more rapid in the winter half of its orbit than in the
summer, by about seven days (see the note to the 6th Geo-
graphical Theorem, p. 4-3.) ; but although in the winter we
are nearer to the sun than in the summer, yet in that
season it seems farthest from us, and the weather is more
cold and inclement ; the simple account of which pheno-
menon is, that the sun's rays falling more perpendicularly
on us in summer, augment the heat of the weather ; so,
being transmitted more obliquely on our parallel of latitude
during the winter, the cold is increased and rendered more
intense. The heat in the torrid zone does not arise from
those parts of the earth being nearer to the sun, but from
the rays of the sun falling perpendicularly upon, and darting
immediately through the atmosphere. It might likewise
be expected that, as we are less distant from the sun in
the winter than in the* summer, it would appear larger ;
but the difference of situation is so small as to make no
sensible alteration in the sun's apparent magnitude.*

The sun is not supposed to be fixed in the centre of
the earth's elliptical orbit, but in one of the foci. Let s
represent the sun (Plate II. Fig. 3.) and AGFBDE the
elliptical orbit of the earth. Then A is called the Peri-
helion, or lower apsis, being the earth's nearest distance
from the sun ; B is called the Aphelion, or higher apsis,
being the greatest distance of the earth from the sun, and
so the distance between the sun (in the focus) and the
centre, is called the eccentricity of the earth's orbit. If
from the centre c there be erected upon the axis AB the
perpendicular CE, meeting the orbit in E, and the line SE
be drawn, it will represent the mean distance of the earth
from the sun, being equal to half the axis AB+, conse-
quently SE is 95 millions of miles.

* The sun's diameter, as measured by the micrometer, is sensibly
larger m perigee than in apogee — ED.

t It is demonstrated by all writers on conic sections, that a line
drawn from one end of the conjugate axis of an ellipsis to the focus, is
equal to half the transverse axis, viz. SE — CB or CA.

Chap. IV. MOTION OF THE EARTH. 71

Though the motion of the earth in its orbit be not uni-
form, yet it is regulated by a certain immutable law, from
which it never deviates ; which is, that a line drawn from
the centre of the sun to the centre of the earth, being
carried about with an angular motion, describes an ellip-
tical area proportional to the time in which that area is
described*, viz. if the times in which the earth moves
from A to E, from E to D, and from D to B, be equal, then
the areas, or spaces, ASE, BSD, and DSB, will all be equal.
The motion of the earth is sometimes quicker and some-
times slower in moving through equal parts of its orbit ;
for when the earth is at A (in the winter) the sun attracts
it more strongly, and therefore the motion is quicker than
any where else ; likewise, when it is at B (in the summer)
it is least affected by the sun's attraction, and conse-
quently the motion there is slower than in any other part
of its orbit, for the power of gravity decreases as the
square of the distance increasesf ; besides it is obvious,
from the construction of the figure, that, if the space ASE
be described in the same time with the space BSD, the arc
AE will be greater than the arc BD.

The phaenomena of the different seasons of the year will
appear plainly from the following observations. Let ABCD
(Plate III. Fig. I.) represent the plane of the earth's
annual orbit, having the sun in the focus F ; and let a b,
an imaginary line passing through the centre of the earth,
be perpendicular to this plane ; also let the axis NS of
the earth make an angle of 23° 28' with this perpendicu-
lar ; then if the earth move in the direction A, B, c, D, in
such a manner that NS may always remain parallel to it-
self, and preserve the same angle with a b, it will point
out the seasons of the year ; for, suppose a line to be
drawn from the centre of the sun to the centre of the
earth, it is evident that the sun will be vertical to that
part of the earth which is cut by this line. Now, when
the earth is in Libra ^ , the sun will appear to be

* This law was discovered by Kepler, and demonstrated by Sir
Isaac Newton. See the Principia, Book III. Prop, xiii.
f Newton's Principia, Book III. Prop. ii.

72 OF THE DIUKNAL AND ANNUAL Part I.

in Aries T, the days and nights will be equal in both
hemispheres, and the season a medium between summer
and winter ; the line dividing the dark and light hemi-
spheres passes through the two poles N and s, and conse-
quently divides all the parallels of latitude, as PR, into two
equal parts ; hence, the inhabitants of the whole face of the
earth have their days and nights equal, viz. twelve hours
each. While the earth moves from Libra £t to Capricorn .
yy, the north pole N will become more and more en-
lightened, and the south pole s will be gradually involved
in darkness, consequently the days in the northern hemi-
sphere will continue to increase in length, and in the
southern hemisphere they will decrease in the same pro-
portion, all the parallels of latitude being unequally di-
vided. When the earth has arrived at Capricorn yj1, the
sun will appear to be in Cancer s> it will be summer to
the inhabitants of the northern hemisphere, and winter to
those in the southern : the inhabitants at the north pole,
and within the arctic circle, will have constant day, and
those at the south pole, and within the antarctic circle, will
have constant night. WThile the earth moves from Capri-
corn Vj> to Aries T, the south pole will become more
and more enlightened; consequently the days in the
southern hemisphere will increase in length, and in the
northern hemisphere they will decrease. When the earth
has arrived at Aries T, the sun will appear to be in
Libra £b, and the days and nights will again be equal all
over the surface of the earth. Again, as the earth moves
from Aries r towards Cancer s, the light will gradually
leave the north pole, and proceed to the south ; when the
earth has arrived at Cancer s, it will be summer to the
inhabitants in the southern hemisphere, and winter to
those in the northern : the inhabitants of the south pole
(if any) will have continual day, those at the north pole
constant night. Lastly, while the earth moves from Can-
cer s to Capricorn \Y, the sun will appear to move from
Capricorn \? to Cancer s, and the days in the northern
hemisphere will be increasing, while those in the southern
will be diminishing in length; and while the earth moves
from Capricorn 13- to Cancer s, the sun will appear to
move from Cancer >s to Capricorn Vf, the days in the

Chap. V. MOTION OF THE EARTH. 73

northern hemisphere will then be decreasing, and those
in the southern hemisphere increasing. In all situations
of the earth, the equator will be divided into two equal
parts, consequently the days and nights at the equator
are always equal. Thus the different seasons are clearly
accounted for, by the inclination of the axis of the earth
to the plane of its orbit *, combined with the parallel
motion of that axis.f

CHAPTER V.

Of the Origin of Springs and Rivers, and of the Saltness
of the Sea.

VARIOUS opinions have been held by ancient as well as
modern philosophers, respecting the origin of springs and
rivers ; but the true cause is now pretty well ascertained.
It is well known that the heat of the sun draws vast quan-

* To shew the obliquity of the axis of the earth to the plane of its
orbit : take a board of any convenient dimensions, suppose two feet
across, on which describe a circle, or an ellipsis differing a little from
a circle, draw a diameter OFO (Plate III. Fig. i.) and parallel to this
diameter let several lines e f be drawn, then bore several holes
perpendicularly down in the point e, e, &c. of the circumference of the
circle ; take two pieces of wire crossing each other in an angle of
23° 28' ; as a g and nf, of which a g the perpendicular wire is the
longer, and connect them by a straight wire ef; then placing a small
globe on the point n, and a light in the centre of the circle of the same
height as the centre of the little globe, let the point g in the longer
wire be fixed successively in the holes e e, &c. in the circumference of
the circle, so that the base ef of the wire may rest on the lines ef'm
the plane of the earth's orbit, the seasons of the year will be agreeably
and accurately illustrated. If the little globe be placed upon the
point a, instead of the point ra, and the same method be observed in
moving the wires round the orbit, there will be no diversity of seasons.
The diurnal revolution of the earth may be shewn by moving the
globe round the wire nf, as an axis, with the finger.

f The phaenomena of the seasons are very familiarly and beautifully
illustrated by the Astronomicon, a machine invented not long since by
Mr. Prior, and published with a course of popular lectures, entitled
" LECTURES ON ASTRONOMY, ILLUSTRATED BY THE ASTRONOMICON,"

74 ORIGIN OF SPRINGS AND RIVERS, AND Part I.

titles of vapour from the sea, which, being carried by the
wind to all parts of the globe, and converted by the
cold into rain and dew, falls down upon the earth : part
of it runs down into the lower places, forming rivulets ;
part serves for the purposes of vegetation, and the rest
descends into hollow caverns within the earth, which
breaking out by the sides of the hills forms little springs ;
many of these springs running into the valleys increase
the brooks or rivulets, and several of these meeting to-
gether make a river.

Dr. Halley * says, the vapours that are raised copiously
from the sea, and carried by the winds to the ridges of
mountains, are conveyed to their tops by the current of
air ; where the water being presently precipitated, enters
the crannies of the mountains, down which it glides into
the caverns, till it meets with a stratum of earth or stone,
of a nature sufficiently solid to sustain it. When this re-
servoir is filled, the superfluous water, following the direc-
tion of the stratum, runs over at the lowest place, and in
its passage meets perhaps with other little streams, which
have a similar origin ; these gradually descend till they
meet with an aperture at the side or foot of the moun-
tain, through which they escape, and form a spring, or the
source of a brook or rivulet. Several brooks or rivulets,
uniting their streams, form small rivers, and these again
being joined by other small rivers, and united in one com-
mon channel, form such streams as the Rhine, Rhone f ,
Danube, &c.

* Philosophical Transactions, No. 192.

t Another very copious source from which the Rhine, the Rhone,
the Danube, and several other rivers derive a very considerable por-
tion of their waters, is the streams which are perpetually flowing from
the beds of the glaciers, or vast seas of ice — mers de glace — which
form so remarkable a feature in Alpine scenery. These streams are
produced by the melting which is continually going on of that part of
the ice which is in contact with the earth's surface beneath these
glaciers.

The following account of Captain Hodgson's tour to discover the
sources of the immense rivers Ganges, Jumna, and Bhagirutta, which
take their rise in the Himmaleh or Himalaya Mountains, is highly
interesting : —

Captain Hodgson left Reital (a village in 30° 48' N.) on the 21st

Chap. V. OF THE SALTNESS OF THE SEA. 75

Several springs yield always the same quantity of water,
equally when the least rain or vapour is afforded, as when
ram falls in the greatest quantities ; and as the fall of rain,
snow, &c. is inconstant or variable, we have here a con-
stant effect produced from an inconstant cause, which is
an unphilosophical conclusion. Some naturalists, there-
fore, have recourse to the sea, and derive the origin of
several springs immediately from thence, by supposing a

of May, 1817. On the 31st he descended to the bed of the river, and
saw the Ganges issue from under a very low arch at the foot of the
grand snow bed. The river was bounded on the right and left by
high rocks and snow, but in front over the debouch6, the mass of snow
was perpendicular ; and from the bed of the stream to the summit the
thickness was estimated at little less than 300 feet of solid frozen snow,
probably the accumulation of ages, as it was in layers of several feet
thick, each seemingly the remains of a fall of a separate year.

From the brow of this curious wall of snow, and immediately
above the outlet of the stream, large and hoary icicles depended. The
height of the arch of snow was barely sufficient to let the stream flow
under it. Blocks of snow were falling on all sides, and there was
little time to do more than measure the size of the stream, the mean
breadth of Which was 27 feet, and its depth varying from 9 to 18
inches. Captain Hodgson believes this to be the first appearance in
day-light of the celebrated Ganges. The height of the halting-place,
near which the Ganges issues from under the great snow-bed, is cal-
culated to be 12914 feet above the sea.

At Jumnoutri, the visible source of the river Jumna, the snow which
covers and conceals the stream is about 60 yards wide, and is bounded
on the right and left by precipices of granite 40^ feet thick, which
have fallen from the precipices above. Captain Hodgson was able to
measure the thickness of the bed of snow over the stream very accu-
rately, by means of a plumb-line let down through one of the holes in
it which are caused by the steam of a great number of boiling springs
at the border of the Jumna. The head of the Jumna is in the S. W.
side of the grand Himalaya range; differing from the Ganges, inas-
much as that river has the upper part of its course within the Hima-
laya, flowing from S.E. to N.W, ; and it is only from Sookie, where
it pierces through the Himalaya, that it assumes a course of about 20
S. W. The mean latitude fcf the hot springs of Jumnoutri appears to
be 30° 58'.

After descending into the bed of the Bhagirutta, that river was also
traced nearly to its source ; the glen through which it runs is deeper
and darker, and the precipices on either side far more lofty than those
forming the bed of the Jumna : the rock in the neighbourhood of its
source was granite, and contained black tourmaline.
E 2

76 ORIGIN OF SPRINGS AND RIVERS, AND Part I.

subterraneous circulation of percolated waters from the
fountains of the deep.

That the sun exhales as much vapour as is sufficient
for rain, is past dispute, having been several times proved
by actual experiments. Dr.Halley* determined by expe-
riment and calculation!, that in a summer's day, there
may be raised in vapours from the Mediterranean 5280
millions of tuns of water, and yet the Mediterranean does
not receive from all its rivers above 1827 millions of tuns
in a day, which is little more than a third part of what is
exhausted by vapours J; and from the river Thames,
twenty millions three hundred thousand tuns may be
raised in one" Say in a similar manner. — In the Old Con-
tinent, there are about 430 rivers which fall directly into
the ocean, or into the Mediterranean and Black Seas, and
in the New Continent, scarcely 180 rivers are known,
which fall directly into the sea; but in this number only
the greater rivers are comprehended.} All these rivers
carry to the sea a great quantity of mineral and saline
particles, which they wash from the different soils through
which they pass, and the particles of salt, which are easily
dissolved, are conveyed to the sea by the water. Dr.
Halley imagines that the saltness of the sea proceeds from
the salts of the earth only, which rivers convey thither,
and that it was originally fresh. So that its saltness will
continue to increase : for, the vapours which are exhaled
from the sea are entirely fresh, or devoid of saline par-
ticles. Others imagine that there is a great number of
rocks of salt at the bottom of the sea, and that from these
rocks it acquires its saltness. Some writers, again, have
imagined that the sea was created salt that it might not
corrupt ; but it may well be supposed that the sea is pre-
served from corruption by the agitations of the wind, and

* Dr. Halley was an eminent mathematician, astronomer, and phi-
losopher, born in London in the year 1656.

f Philosophical Transactions, No. 212.

J As evaporation cannot carry off fixed salts, it would appear that if
the above calculation be accurate, the Mediterranean would be more
salt than the ocean; but it must be remembered that a current seta
constantly out of the Atlantic Ocean into the Mediterranean.

§ Buffon's Natural History.

Chap. V. OF THE SALTNESS OF THE SEA. 77

by the flux and reflux of the tide, as much as by the
salt it contains ; for, when sea-water is kept in a barrel, it
corrupts in a few days. The Honourable Mr. Boyle * re-
lates that a mariner, becalmed for thirteen days, found at
the end of that time, the sea so infected, that if the calm
had continued, the greatest part of his people on board
would have perished. — The sea is nearly equally salt,
throughout, under the equinoctial line and at the Cape of
Good Hope, though there are some places on the Mo-
zambique coast where it is salter than elsewhere. It is
also asserted that it is not quite so salt under the arctic
circle as in some other latitudes -j- ; this probably may pro-
ceed from the great quantity of snow, and the great rivers
which fall into those seas : to which we may add, that the
sun does not draw such quantities of fresh^water, or va-
pours, from those seas as in hot countries.

It is worthy of remark, that all lakes from which rivers
derive their origin, or which fall into the course of rivers,
are not saline £ ; and almost all those, on the contrary,
which receive rivers, without other rivers issuing from
them, are saline: this seems to favour Dr. Halley's
opinion respecting the saltness of the sea ; for evaporation
cannot carry off fixed salts, and consequently those salts
which rivers carry into the sea remain there. It is as-
serted § to be the peculiar property of sea-water, that
when it is absolutely salt it never freezes ; and that the
islands or rocks of ice which float in the sea near the
poles, are originally frozen in the rivers, and carried
thence to the sea by the tide ; where they continue to
accumulate by the great quantities of snow and sleet
which fall in those seas. According to this opinion, great
quantities of ice can be produced only from great quan-

* A younger son of the Earl of Cork, and one of the most cele-
brated philosophers in Europe, born at Lismore, in the county of
Waterford, 1626-7. See his treatise on the Saltness of the Sea, pub-
lished in 1674.

f In a System of Chemistry, by Dr. Thomson, of Edinburgh, Vol.iv.
fourth edition, page 141, it is stated, that the ocean contains most salt
between 10° and 20° south latitude, and that the proportion of salt is
the least in latitude 57° north.

$ Buffon's Natural History, Chap. II.

§ Emerson's Geography, page 64.
E 3

78 OF THE FLUX AND Parti.

titles of fresh water, or from large rivers, and as large
rivers can only flow from large tracts of land, it would
appear that there must be immense tracts of land near
the south pole, for the Antarctic Ocean abounds with
fields or mountains of ice, as well as the Arctic Ocean ;
but our circumnavigators have traversed the Southern
Ocean to upwards of seventy degrees south latitude,
without discovering any land. * With respect to the
freezing of salt water, we have several instances of the
Baltic f and other seas being frozen over, when the ice
on the surface could never proceed from rivers. It is
true that the sailors frequently take large pieces of the
rocks of ice, and thaw them for the use of the ship's com-
pany, and always find the water fresh ; but it does not
follow from this that the ice is formed in the rivers. As
fresh water only is extracted from sea-water by the heat
of the sun, and carried into the atmosphere ; may not the
fresh, without the saline particles of sea-water, be con-
verted into ice by extreme cold ?

CHAPTER VI.
Of the Flux and Reflux of the Tides.

A TIDE is that motion of the water in the seas and
rivers, by which they are found to rise and fall in a regu-

* Mr. William Smith, master of the brig Williams, of Blythe, Nor-
thumberland, in a voyage from Buenos Ayres to Valparaiso, in Chili,
in order more easily to weather Cape Horn, steered an unusual
southerly course, and on the 19th of February 1819, lat. 62° 17' S.
long. 60° 12' W. discovered land : he afterwards ascertained the ex-
istence of the coast for the distance of 250 miles. An account of this
discovery, with plates of the appearance of the land, &c. may be seen
in the Edinburgh Philosophical Journal, Vol. III. October 1820.
page 367. This newly-discovered land is called New South Shetland.

t The Baltic Sea is not so salt as the ocean, and the proportion of
salt is increased by a west wind, and still more by a north-west wind :
a proof that not only the saltness of the Baltic is derived from the
ocean, but that storms have a much greater effect upon the v/aters of
the ocean than has been supposed . Dr. Thomsons Chemistry, vol. iv.

page 141 The Baltic Sea has little or no tides, and a current runs

constantly through the Sound into the Cattegate sea.

Chap. VI. HEFLUX OF THE TIDES. 79

lar succession ; and this flowing and ebbing is caused by
the attraction of the sun and moon. *

Suppose the earth to be entirely covered by a fluid as
A, B, z, c, D, a, N. (Plate III. Figure 2.) and the action
of the sun and moon to have no effect upon it, then it is
evident that all the particles, being equally attracted to-
wards the centre o of the earth, would form an exact
spherical surface ; except, that by the revolution of the
earth on its axis N s , the attraction from B towards o,
and from Q towards o would be a little diminished by the
centrifugal force. Let the moon at M now exert her in-
fluence upon the water ; then because the power of at-
traction diminishes as the square of the distance increases,
those parts will be the most attracted which are the
nearest to the moon, and their tendency towards o will
be diminished : the waters at z, B, and c, will therefore
rise, and at z, which is nearest to the moon, they will be
the highest: but when the waters in the zenith z are
elevated, those in the nadir N are likewise elevated in a
similar manner ; this is known from experience, for we
have high water when the moon is in our nadir, as well as
when she is in our zenith; we therefore conclude that,
when the moon is in our zenith, our antipodes have high
water : the truth of this, as well as every other pheno-
menon respecting the tides, will be discussed in the follow-
ing theorems.

THEOREM I.f The parts of the earth directly under the
moon, or where the moon is in the Zenith as at z (Plate
III. Figure 3.) ; and those places which are diametrically
opposite to the former, or under the Nadir as at N, will
have high water at the same time.

Because the power of gravity decreases as the square
of the distance increases ; the waters at A, B, z, c, D, on

* This was known to the ancients : Pliny expressly says that the
cause of the ebb and flow is in the sun, which attracts the waters of the
ocean, and that they also rise in proportion to the proximity of the
moon to the earth. Dr. Buttons. Math. Dictionary, word Tides.

f A theorem is a proposition which admits of proof, or demonstra-
tion, from definitions clearly understood, and from the known general
properties of the subject under consideration.
E 4*

80 OF THE FLUK AND Part I.

the side of the earth next the moon M, will be more
attracted by the moon than the central parts o of the
earth, and the central parts will be more attracted than
the surface N on the opposite side of the earth ; therefore
the distance between the centre of the earth and the
surface of the water, under the zenith and nadir, will be
increased. For, let three bodies z, o, and N, be equally
attracted by M; then it is evident they will all move
equally fast, to wards M, and their mutual distances from
each other will continue the same ; but if the bodies be
unequally attracted by M, that body which is the most
attracted will move the fastest, and its distance from the
other bodies will be increased. Now, by the law of gra-
vitation, M will attract z more strongly than it does o, by
which the distance between z and o will be increased.
In like manner o being more strongly attracted than N,
the distance between o and N will be increased : suppose
now a number of bodies, A, B, z, c, D, F, N, E, placed
round o, to be attracted by M, the parts z and N will have
their distances from o increased ; while the parts A and
D, being nearly at the same distance from M as o is, will
not recede from each other, but will rather approach
near to o by the oblique attraction of M. Hence if
the whole earth were composed of bodies similar to A, B,
z, c, D, F, N, E, and were similarly attracted by M, the
section of the earth, formed by a plane passing through
the moon and the earth's centre, would be a figure re-
sembling an ellipsis, having its longer axis ZN directed
towards the moon ; and its shorter axis AD in the horizon.
The figure of the earth, therefore, would be an oblong
spheroiti, having its longer axis directed to the moon,
consequently it will be high water in the zenith and na-
dir at the same time ; and as the earth turns round its
axis from the moon to the moon again in about 24 hours
and 48 minutes, there will be two tides of flood and two
of ebb in that time, agreeably to experience.

According to the foregoing explanation of the ebbing
and flowing of the sea, every part of the earth is gravi-
tating towards the moon ; but as the earth revolves round
the sun, every part of it gravitates towards the sun like-
wise ; it may be asked hoM' is this possible at the time of

Chap. VI. REFLUX OF THE TIDES. 81

full moon, when the moon is at m and the sun at s ; has
the earth a tendency to fall contrary ways at the same
time ? This is a very natural question ; but it must be
considered that it is not the centre of the earth that de-
scribes the annual orbit round the sun, but the common
centre of gravity of the earth and moon together ; and
that whilst the earth is moving round the sun, it also de-
scribes a circle round that centre of gravity, about which
it revolves as many times as the moon revolves round the
earth in a year. * The earth is therefore constantly falling
towards the moon, from a tangent to the circle which
it describes round the common centre of gravity of the
earth and moon. Let M represent the moon (Plate III.
Figure 4.), TW a part of the moon's orbit, and as the
earth is supposed to contain about forty times the quantity
of matter which is contained in the moon, the common
centre of gravity from the centre of the earth towards the
moon will be considerably less than the earth's diameter-j-,
let this common centre of gravity be represented by c.
Then whilst the moon goes round her orbit, the centre of
the earth describes the circle doe round c, to which cir-

* Ferguson's Astronomy, article 298.

f The common centre of gravity of two bodies is found thus : as
the sum of the weights or quantities] of matter in the two bodies is to
their distance from each other, so is the weight of the less body to
the distance of the greater from the centre of gravity. Now if the
quantity of matter in the moon be represented by 1, that in the
earth by 40, and the distance of the earth from the moon be esti-
mated at 240,000 miles, then 40 + 1 : 240,000 : : 1 : 5853 miles, the
distance of the centre of the earth from the common centre of gravity.
Mr. A. Walker, in the llth lecture of his Familiar Philosophy, inge-
niously accounts for its being high-water in the zenith and nadir at the
same time, in the following manner : — " The parts of the earth that
" are farthest from the moon, will have a swifter motion round the
" centre of gravity than the other parts ; thus the side n will describe
" the circle n v. y, while the side m will only describe the small circle
" m r s, round the centre of gravity c. Now, as every thing in
" motion always endeavours to go forward in a straight line, the water
" at n having a tendency to go off in the line n q, will in a degree
" overcome the power of gravity, and swell into a heap or protuberance,
" as represented in the figure, and occasion a tide opposite to that
" caused by the attraction of the moon."
E 5

82 OF THE FLUX AND Part I.

cle o a is a tangent : therefore when the moon has gone
from M to a little past w, the earth has moved from o to
e ; and in that time has fallen towards the moon from the
tangent at a to e. This figure is drawn for the new moon,
but the earth will tend towards the moon in the same
manner during its whole revolution round c.

THEOREM II. Those parts of the earth where the moon
appears in the horizon, or 90 degrees distant from the
Zenith and Nadir, as at A and D (Plate III. Figure 3.)
will have ebb or low water.

For, as the waters under the zenith and nadir rise at the
same time, the waters in their neighbourhood will press
towards those places to maintain the equilibrium ; and to
supply the place of these waters, others will move the
same way, and so on to places of 90 degrees distance
from the zenith and nadir; consequently at A and D,
where the moon appears in the horizon, the waters will
have more liberty to descend towards the centre of the
earth ; and therefore in those places they will be the
lowest. Hence it plainly appears, that the ocean, if it
covered the whole surface of the earth, would be a sphe-
roid (as was observed in the foregoing theorem), the
longer diameter as ZN passing through the place where
the moon is vertical, and the shorter diameter as AD
passing through the rational horizon of that place. And
as the moon apparently * shifts her position from east to
west in going round the earth every day, the longer dia-
meter of the spheroid following her motion will occasion
the two floods and ebbs in about 24 hours and 48 mi-
nutes f, the time which any meridian of the earth takes

* The real motion of the moon is from the west towards the east ;
for if she be seen near any fixed star on any night, she will be seen
about 13 degrees to the eastward of that star the next night, and so
on. The moon goes round her orbit from any fixed star to the same
again in 27 d. 7h. 43m. 11.5s. Hence 27 d. 7 h. 43m. 11. 5s. :
360° : : 1 d. : 13° 10' 34".68 the mean motion of the moon in 24
hours.

f The mean motion of the moon in 24 hours is 13° 10' 34". 68 and
the mean apparent motion of the sun in the same time is 59' 8". 3.

Chap. VI. REFLUX OF THE TIDES. 83

in revolving from the moon to the moon again ; or the
time elapsed (at a medium) between the passage of the
moon over the meridian of any place, and her return to
the same meridian.

The meridian altitude of the moon at any place is her
greatest height above the horizon at that place, hence
the greater the moon's meridian altitude is, the greater
the tides will be ; for they increase from the horizon D
to the point z under the zenith, and the greater the
moon's meridian depression is below the horizon, the
greater the tides will be ; for they increase from the hori-
zon D towards N, the point below the nadir, and conse-
quently as the tides increase from D to N, the tides in
their antipodes will increase from A to z.

THEOREM III. The time of high water is not precisely at
the time of the moons coming to the meridian, but about
an hour after.

For, the moon acts with some force after she has passed
the meridian, and by that means adds to the libratory or
waving motion, which the waters had acquired whilst she
was on the meridian.

THEOREM IV. The tides are greater than ordinary twice
every month ; viz. at the time of new and full moon, and
these are called SPRING-TIDES. (Plate III. Figure III.)

For at these times the actions of both the sun and
moon concur to draw in the same straight line SMZON,
and therefore the sea must be more elevated. In con-
junction, or at the new moon when the sun is at s and the
moon at M, both on the same side of the earth, their joint
forces conspire to raise the water in the zenith at z, and
consequently (according to Theorem I.) at N the nadir

(see the note to definition 61. page 14.) the moon's motion is therefore
12° 1 1' 26".38 swifter than the apparent motion of the sun in one day,
which, reckoning 4 minutes to a degree, amounts to nearly 48 mi-
nutes 46 seconds of time.

E 6

84 OF THE FLUX AND Part I.

likewise.* When the sun and moon are in opposition,
or at the full moon when the sun is at s and the moon at
m, the earth being between them ; while the sun raises
the water at z under the zenith and at N under the nadir,
the moon raises the water at N under the nadir and at z
under the zenith.

* Mr. Walker says (Lecture llth), that at new moon, " The sun's
" influence is added to that of the moon, and the centre of gravity c
" (Plate III. Figure 4.) will, therefore, be removed farther from the
" earth than we, and of course, increase the centrifugal tendency of
" the tide n : hence both the attracted and centrifugal tides are spring-

" tides at that time." " But spring-tides take place at the full as

*' well as at the change of the moon. Now it has been premised, that
" if we had no moon, the sun would agitate the ocean in a small de-
" gree and make two tides every twenty-four hours, though upon a
" small scale. The moon's centrifugal tide at z (Plate III. Figure 3.)
" being increased by the sun's attraction at , s, will make the protu-
" berance a spring-tide ; and the sun's centrifugal tide at N will be re-
" inforced by the moon's attraction at m, and make the protuberance
" N a spring-tide ;• so spring-tides take place at the full as well as

" change of the moon." Suppose the moon to be taken away

(Plate III. Figure 4.) the common centre of gravity of the earth and
the sun would fall entirely within the body of the sun, round which
the earth revolves in a year, at the rate of about a degree in a day ;
hence the parts n of the earth farthest from the sun would have a little
more tendency to recede from the centre of motion s, than the parts m
which are the nearest. So that if the sun were on the meridian of any
place, it would be high water at that place by the sun's attraction, and
it would at the same time be high water at the antipodes of that place
by the centrifugal tendency ofra; consequently, as the earth revolves on
its axis from noon to noon in 24 hours, there would be two tides of
flood and two of ebb during that time. If the line m c be increased
when the moon is in conjunction with the sun, so as to cause the point
n to describe a larger circle than n v Y, and also the point m to describe
a larger circle than m r s round the centre of gravity c ; when the sun
is in opposition to the moon, the line m c will be diminished, n will
therefore describe a smaller circle than n v Y, and m will describe a
smaller circle than m r s. Hence it appears that the centrifugal tend-
ency of n is greater at the new moon than it is at the full moon, and
m is likewise more strongly attracted at the same time ; the spring-tides
at the time of conjunction would therefore be considerably greater than
at the time of opposition, were not the moon's centrifugal tide at this
time attracted by the sun, and the sun's centrifugal tide added to that
caused by the moon's attraction.

I. REFLUX OF THE TIDES. 85

THEOREM V. The tides are less than ordinary twice every
month ; that is, about the time of the first and last
quarters of the moo?i, and these are called NEAP-TIDES,
(Plate III. Figure 3.)

Because in the quadratures, or when the moon is 90
degrees from the sun, the sun acts in the direction SD,
and elevates the water at D and A ; and the moon acting
in the direction MZ or mx elevates the water at z and N ;
so that the sun raises the water where the moon depresses
it, and depresses the water where the, moon raises it ;
consequently the tides are formed only by the difference
between the attractive force of the sun and moon. — The
waters at z and N will be more elevated than the waters
at D and A, because the moon's attractive force is four *
times that of the sun.

THEOREM VI. The spring-tides do not happen exactly on
t/ie day of the change or full moony nor the neap-tides
exactly on the days of the quarters, but a day or two
afterwards.

When the attractions of the sun and moon have con-
spired together for a considerable time, the motion im-
pressed on the waters will be retained for some time after

* Sir Isaac Newton, Cor. 3. Prop. XXXVII. Book III. Principia
makes the force of the moon to that of the sun, in raising the waters of
the ocean, as 4.4815 to 1 : and in Corol. 1. of the same proposition he
calculates the height of the solar tide to be 2 feet 0 inch 4, the lunar
tide 9 feet 1 inch ^, and by their joint attraction 1 1 feet 2 inches ; when
the moon is in Perigee the joint forces of the sun and moon will raise
the tides upwards of 13J feet. — Sir Isaac Newton's measures are in
French feet in the Principia. I have turned them into English feet.

Mr. Emerson, in his Fluxions, Section III. Prob. 25. calculates the
greatest height of the solar tide to be 1.G3 feet, the lunar tide 7.2H feet,
and by their joint attraction 8.91 feet, making the force of the sun to
that of the moon as 1 to 4.4815.

Dr. Horsley, the late bishop of St. Asaph, estimates the force of the
moon to that of the sun as 5.0469 to 1. Sec his edition of the Prin-
cipia, lib. 3. Sect 3. Prop. XXXVI. and XXXVII.

Mr. Walker, in Lect. 1 1th of his Familiar Philosophy, states the
influence of the sun to be to the influence of the moon to raise the
water, as 3 is to 10, and their joint force 13.

86 OF THE FLUX AND Part I.

their attractive forces cease, and consequently the tide
will continue to rise. In like manner at the quarters,
the tide will be the lowest when the moon's attraction has
been lessened by the sun's for several days together. — If
the action of the sun and moon were suddenly to cease,
the tides would continue their course for some time, as
the waves of the sea continue to be agitated after a storm.

THEOREM VII. When the moon is nearest to the earth, or
in Perigee, the tides increase more than in similar cir-
cumstances at other times.

For the power of attraction increases as the square of
the distance of the moon from the earth decreases ; con-
sequently the moon must attract most when she is nearest
to the earth.

THEOREM VIII. The spring tides are greater a short time
before the vernal equinox, and after the autumnal equinox,
viz. about the latter end of March and September* than
at any other time of the year. (Plate III. Fig. III.)

Because the sun and moon will then act upon the
equator in the direction a f B, consequently the sphe-
roidal figure of the tides will then revolve round its longer
axis, and describe a greater circle than at any other time
of the year ; and as this great circle is described in the
same time that a less circle is described, the waters will
be thrown more forcibly against the shores in the former
circumstances than in the latter.

THEOREM IX. Lakes are not subject to tides ; and small
inland seas, such as the Mediterranean and Baltic, are
little subject to tides. In very high latitudes north or
south the tides are also inconsiderable.

The lakes are so small, that when the moon is vertical
she attracts every part of them alike. The Mediterra-
nean and Baltic seas have very small elevations, because
the inlets by which they communicate with the ocean are
so narrow, that they cannot, in so short a time, receive or
discharge enough to raise or lower their surfaces sensibly

Chap. VI. REFLUX OF THE TIDES. 87

THEOREM X. The time and height of the tides may be
very different according to the situations of places.

In some places, the tide-wave, rushing up a narrow
channel, is suddenly raised to an extraordinary height.
At Annapolis, in the Bay of Fundy, it rises 120 feet.
Even at Bristol, the difference of high and low water
occasionally amounts to 50 feet. — Sir J.F. W.Herschel.

GENERAL OBSERVATIONS.

The new and full moon spring-tides rise to different
heights.

The morning tides differ generally in their rise from the
evening tides.

In winter the morning tides are highest.

In summer the evening tides are highest.

The tides follow, or flow towards the course of the
moon, when they meet with no impediment. Thus the
tide on the coast of Norway flows to the south (towards
the course of the moon) ; from the North-cape in Norway
to the Naze at the entrance of the Scaggerac, or Catte-
gat Sea, where it meets with the current which sets
constantly out of the Baltic Sea, and consequently pre-
vents any tide rising in the Scaggerac. The tide pro-
ceeds to the southward, along the east coast of Great
Britain, supplying the ports successively with high water,
beginning first on the coast of Scotland. Thus it is high
water at Tynemouth Bar, at the time of new and full
moon, about three hours after the time of high water at
Aberdeen ; it is high water at Spurn-head about two
hours after the time of high-water at Tynemouth Bar ; in
an hour more it runs down the Humber, and makes high
water at Kingston upon Hull ; it is about three hours
running from Spurn-head to Yarmouth Road, one hour
in running from Yarmouth Road to Yarmouth Pier ;
2^ hours running from Yarmouth Road to Harwich, 1£
hour in passing from Harwich to the Nore, from whence it
proceeds up the Thames to Gravesend and London. From
the Nore the tide continues to flow southward to the
Downs and Goodwin Sands, between the North and South
Foreland in Kent, where it meets the tide which flows
out of the English Channel through the Strait of Dover.

88 OF THE FLUX AND Part I.

While the tide, or high water, is thus gliding to the
southward along the eastern coast of Great Britain, it
also sets to the southward along the western coasts of
Scotland and Ireland; but, on account of the obstruc-
tions it meets with from the Western Islands of Scotland,
and the narrow passage between the north-east of Ireland
and the south-west of Scotland, the tide in the Irish
Sea comes round by the South of Ireland through St.
George's Channel, and runs in a north-east direction till
it meets the tide between Scotland and Ireland at »the
north-west part of the Isle of Man. This may be na-
turally inferred from its being high water at Waterford
above three hours before it is high water at Dublin, and
it is high water at Dundalk Bay and the Isle of Man
nearly at the same time. That the tide continues its
course southward may be inferred from its being high
water at Ushant, opposite to Brest in France, about an
hour after the time of high water at Cape Clear, on the
southern coast of Ireland. Between the Lizard Point in
Cornwall and the island of Ushant, the tide flows east-
ward, or east-north-east, up the English Channel, along
the coasts of England and France, and so on througli
the Strait of Dover, till it comes to the Goodwin Sands
or Galloper, where it meets the tide on the eastern
coast of England, as has been observed before. The
meeting of these two tides contributes greatly towards
sending a powerful tide up the river Thames to London ;
and, when the natural course of these two tides has been
interrupted by a sudden change of the wind, so as to
accelerate the tide which it had before retarded, and to
drive back that tide which had before been driven
forward by the wind, this cause has been known to pro-
duce twice high water in the course of three or four
hours. The above account of the British tides seems to
contradict the general theory of the motion of the tides,
which ought always to follow the moon, and flow from
east to west; but to allow the tides their full motion,
the ocean in which they are produced ought to extend
from east to west at least 90 degrees, or 6255 English
miles; because that is the distance between the places
where the water is the most raised and depressed by the

Chap. VII. REFLUX OF THE TIDES. 89

moon. Hence it appears that it is only in the great oceans
that the tide can flow regularly from east to west ; and
hence we also see why the tides in the Pacific Ocean ex-
ceed those in the Atlantic, and why the tides in the torrid
zone between Africa and America, though nearly under
the moon, do not rise so high as in the temperate zones
northward and southward, where the ocean is consider-
ably wider. The tides in the Atlantic, in the torrid zone,
flow from east to west till they are stopped by the con-
tinent of America ; and the trade winds likewise continue
to blow in that direction. When the action of the moon
upon the waters has in some degree ceased, the force of
the trade winds, in a great measure, prevents their return
towards the African shores. The waters thus accumu-
lated* in the gulf of Mexico return to the Atlantic be-
tween the island of Cuba, the Bahama islands, and East
Florida, and form that remarkably strong current called
the gulf of Florida.

CHAPTER VII.

Of the natural Changes of the Earth, caused by Mountains,
Floods, Volcanoesy and Earthquakes.

THAT there have always been mountains from the
foundation of the world, is as certain as that there have
always been rivers, both from reason and revelation t;
for they were as necessary before the flood for every
purpose as they are at present. If the earth were per-
fectly level, there could be no rivers, for water can flow

* To show that an accumulation of water does take place in the
gulf of Mexico, a survey was made across the isthmus of Darien ;
when the water on the Atlantic was found to be fourteen feet higher
than the water on the Pacific side. Walker's Familiar Philosophy,
lecture xi.

t Four rivers, or rather four branches of one river, are expressly
mentioned before the flood, viz. Pison, Gihon, Hiddekel, and the
Euphrates. Genesis, chap. ii. And in the 7th chapter of Genesis, at
the time of the flood, we are told that the fountains of the great deep
were broken up, the windows of heaven were opened, the waters pre-
vailed exceedingly upon the earth, and all the high hills and the
mountains were covered.

90 NATURAL CHANGES OF THE EARTH, Part I.

only from a higher to a lower place ; and instead of that
beautiful variety of'hills and valleys, verdant fields, forests,
&c. which serve to display the goodness and beneficence
of the Deity, a dismal sea would cover the whole face of
the earth, and render it at best an habitation for aquatic
animals only.

All mountains and high places continually decrease in
height. Rivers running near mountains undermine and
wash a part of them away, and rain falling on their sum-
mits washes away the loose parts, and saps the found-
ations of the solid parts, so that, in the course of time, they
tumble down. Thus, old buildings on the tops of moun-
tains are observed to have their foundations laid bare by
the gradual washing away of the earth. In plains and
valleys we find a contrary effect ; the particles of earth
washed down from the hills, fill up the valleys, and an-
cient houses built in low places seem to sink. For the
same reason a quantity of mud, slime, sand, earth, &c.
which is continually washed down from the higher places
into the rivers, is carried by the stream, and by degrees
choaks up the mouths of rivers, especially when the soil
through which they run is of a loose and rich quality.
Thus, the water of the river Mississippi, though wholesome
and well tasted, is so muddy, that a sediment of two inches
of slime has been found in a half-pint tumbler of it * : this
river is choaked up at the mouth with the mud, trees, &c.
which are washed down it by the rapidity of the current.

The highest mountains in the world, except the
Himalaya, are the Andes f , in South America, which ex-
tend near 4300 miles in length, from the province of
Quito to the strait of Magellan : the highest, called Sorata
in Bolivia, or Upper Peru, is said to be 25,250 feet, or

* Morse's American Geography.

f The Himmaleh or Himalaya mountains (the abode of snow} exceed
in height the Andes, or any other mountains on the face of the globe.
The highest mountain in the world is Chimularee, one of the Himalaya
mountains north of Hindostan, the most elevated part of its summit is
said to be about 29,000 feet. The next highest is Dhawalagiri, which
is 28,015 feet above the level of the sea. There are no glaciers in
any part of the snowy mountains, but a perpetual frost appears to

Chap. VII. BY MOUNTAINS, FLOODS, &C. 91

nearly five miles above the level of the sea. The next
highest of these mountains is Illimani, Peru ; the summit
of which exceeds 24,000 feet. Chimborazo, which was
formerly supposed to be the highest of the Andes, is only
21, 440 feet ; 5000 of which, from the summit, are always
covered with snow. From experiments made with a
barometer * on the mountain Cotopaxi, another part of
the Andes, it appeared that its summit is elevated 6252
yards, or upwards of 3j miles. The Peak of Teneriffe,
in the island of that name, is said to be 13,265 feet, or
upwards of 2-J miles high. Mont Blanc, the highest
mountain in Europe, is 15,304 feet above the level of the
sea. These irregularities, although very considerable
with respect to us, are nothing when compared with the
magnitude of the globe. Thus, if an inch were divided
into one hundred and eleven parts, the elevation of Chim-
borazo, on a globe of eighteen inches in diameter, would
be represented by one f of these parts.

Hence the earth, which appears to be crossed by the
enormous height of mountains, and cut by the valleys

rest on their summits. The following is a list of the altitudes of a
few of the most elevated mountains in the four quarters of the world : —

MOUNTAINS. SITUATION. FEET.

1. Chimularee (Himalaya), N. of Industan - 29,000

2. Dhawalagiri (ditto), - ditto - - - 28,015

3. Javahar - - (ditto), - - ditto - 25,800

4. Sorata (Andes), - - Bolivia, Peru • •• V -25,250

5. Illimani, (ditto), - - - ditto - -24,450

6. Chimborazo (ditto), - - ditto - 21,440

7. Cotopaxi (ditto), - - Colombia * 18,89O

8. Mont Blanc (Alps'), - Savoy - -...-'..' - 15,781

9. Mont Rosa (Alps'), - Switzerland - ' -, - 15,527
10. Mount Hentet (Atlas Range), Moroco - 15,000

* The quicksilver in a barometer falls about 1 -tenth of an inch
every 32 yards of height ; so that if the quicksilver descends 3-tenths
of an inch, in ascending -a hill, the perpendicular height of that hill
will be 96 yards. This method is liable to error. See the Causes
which affect the Accuracy of Barometrical Experiments, in the Edin-
burgh Philosophical Transactions, by Mr. Playfair; also in Keith's
Trigonometry, fourth edition, p. 97.

f See the note (Chap. III. p. 59.) of the Figure of the Earth.

92 NATURAL CHANGES OF THE EARTH, Part I.

and the great depth of the sea, is nevertheless, with re-
spect to its magnitude, only very slightly furrowed with
irregularities, so trifling indeed as to cause no difference
in its figure.

Having, in some measure, accounted for the descend-
ing oi' the earth from the hills, and filling up the valleys,
stopping the mouths of rivers, &c. which are gradual,
and much the same in all ages, the more remarkable
changes may be reduced to two general causes, floods
and earthquakes.

The real or fabulous deluges mentioned by the an-
cients may be reduced to six or seven, and though some
authors have endeavoured to represent them all as im-
perfect traditions of the universal deluge recorded in the
sacred writings, the Abbe Mann *, from whom the follow-
ing observations are extracted, does not doubt but that
they refer to various real and distinct events of the kind.t

1. The submersion of the Atlantis of Plato probably
was the real subsidence of a great island stretching from
the Canaries to the Azores, of which those groups of
small islands are the relics.

2. The deluge in the time of Cadmus and Dardanus
placed by the best chronologists in the year before Christ
1477, is said by Diodorus Siculus to have inundated
Samothrace, and the Asiatic shores of the Euxine Sea.

3. The deluge of Deucalion, which the Arundelian
marbles {, or the Parian chronicles, fix at 1529 years be-
fore Christ, overwhelmed Thessaly.

4. The deluge of Ogyges, placed by Acusilaus in the
year answering to 1796 before Christ, laid waste Attica

* Vide Nouveaux Memoires de 1' Academic Imperiale et Royale
de Sciences et des Belles Lettres, de Brussels, tome premier, 1788.

f M. Biot has discovered, in the annals of the Chinese, historic evi-
dences of two great deluges, the most recent of which they place as
far back as the 23d century before our era.

\ Ancient stones, whereon is inscribed a chronicle of the city of
Athens, engraven in capital letters, in the island of Paros, one of the
Cyclades, 264 years before Christ. They take their name from
Thomas, Earl of Arundel, who procured them from the East. They
were presented to the University of Oxford in the year 1667, by the
Hon. Henry Howard, afterwards Duke of Norfolk, grandson to the
first collector of them.

Chap. VII. BY MOUNTAINS, FLOODS, &C. 93

and Bceotia. With the poetical and fabulous accounts
of Deucalion's flood are mingled several circumstances of
the universal deluge ; but the best writers attest the
locality and distinctness, both of the flood of Deucalion
and Ogyges.

5. Diodorus Siculus, after Manetho, mentions a flood
which inundated all Egypt in the reign of Osiris ; but, in
the relations of this event, are several circumstances re-
sembling the history of Noah's flood.

6. The account given by Berosus the Chaldean of an
universal deluge in the reign of Xisuthrus, evidently re-
lates to the same event as the flood of Noah.

7. The Persian Guebres, the Brahmins, Chinese, and
Americans, have also their traditions of an universal
deluge. The account of the deluge in the Koran has
this remarkable circumstance, that the waters which
covered the earth are represented as proceeding from
the boiling over of the cauldron*, or oven, Tannour,
within the bowels of the earth: and that, when the
waters subsided, they were swallowed up again by the
earth.

The Abbe next gives a summary of the Scripture ac-
count of Noah's flood, and points put very clearly that
part of the waters came from the atmosphere, and part
from under ground agreeably to the llth verse of the
viith chapter of Genesis.

Earthquakes are another great cause of the changes
made in the earth. From history we have numerous
instances of the dreadful and various effects of these ter-
rible phenomena. Pliny has not only recorded several
extraordinary phenomena which happened in his own
time, but has likewise borrowed many others from the
writings of more ancient nations.

1. A city of the Lacedemonians was destroyed by an
earthquake, and its ruins wholly buried by the mountain
Taygetus falling down upon them, f

*• This circumstance is mentioned here, because it agrees with Mr.
Whitehurst's Theory of the Earth; he supposes the flood was occasioned
by the expansive force of fire generated at the centre of the earth.

t Pliny's Natural History, chap. 79.

94 NATURAL CHANGES OF THE EARTH, Part I.

2. In the books of the Tuscan learning an earthquake
is recorded, which happened within the territory of
Modena, when L. Martius and S. Julius were consuls,
which repeatedly dashed two hills against each other ;
with this conflict all the villages and many cattle were
destroyed.

3. The greatest earthquake mentioned in history was
that which happened during the reign of Tiberius Caesar,
when twelve cities of Asia were laid level in one
night. *

4. The eruption of Vesuvius, in the year 79 f , over-
whelmed the two famous cities of Herculaneum J and
Pompeii, by a shower of stones, cinders, ashes, sand, &c.
and totally covered them many feet deep, as the people
were sitting in the theatre. The former of these cities
was situated about four miles from the crater, and the
latter about six.

By the violence of this eruption, ashes were carried
over the Mediterranean Sea into Africa, Egypt, and
Syria : and at Rome they darkened the air on a sudden,
so as to hide the face of the sun. §

5. In the year 1533, large pieces of rock were thrown
to the distance of fifteen miles, by the volcano Cotopaxi
in Peru. ||

6. On the 29th of September 1535, previous to an
eruption near Puzzoli, which formed a new mountain of
three miles in circumference, and upwards of 1200 feet
perpendicular height, the earth frequently shook, and the
plain lying between the lake Averno, mount Barbaro, and
the sea was raised a little ; at the same time the sea, which
was near the plain, retired two hundred paces from the
shore.

* Pliny, chap. 84.

^ t Pliny lost his life by this irruption, from too eager a curiosity in
viewing the flames.

| This city was discovered in the year 1736, eighty feet below the
surface of the earth ; and some of the streets of Pompeii, &c. have since
been discovered.

§ Burnet's Sacred History, p. 85. vol. ii.

|| Ulloa's Voyage to Peru, vol. i. p. 324.

<f Sir William Hamilton's Observations on Vesuvius.

Chap. VII. BY MOUNTAINS, FLOODS, &C. 95

7. In the year 1538, a subterraneous fire burst open
the earth near Puzzoli, and threw such a vast quantity of
ashes and pumice stones, mixed with water, as covered
the whole country, and thus formed a new mountain, not
less than three miles in circumference, and near a quarter
of a mile perpendicular height. Some of the ashes of this
volcano reached the vale of Diana, and some parts of
Calabria, which are more than one hundred and fifty
miles from Puzzoli.*

8. In the year 1538, the famous town called St.
Euphemia, in Calabria Ulterior, situated at the side
of the bay under the jurisdiction of the knights of
Malta, was totally swallowed up with all its inhabitants,
and nothing appeared but a fetid lake in the place of
it.f

9. A mountain in Java, not far from the town of Pana-
cura, in the year 1586, was shattered to pieces by a vio-
lent eruption of glowing sulphur (though it had never
burnt before,) whereby ten thousand people perished in
the underland fields. ^

10. In the year 1600, an earthquake happened at
Arquepa in Peru, accompanied with an irruption of sand,
ashes, &c. which continued during the space of twenty
days, from a volcano breaking forth; the ashes falling
in many places above a yard thick, and in some places
more than two, and where least, above a quarter of a yard
deep, which buried the corn grounds of maize and wheat.
The boughs of trees were broken, and the cattle died for
want of pasture; for the sand and ashes thus erupted,
covered the fields ninety miles one way, and one hundred
and twenty another way. During the eruption, mighty
thunders and lightnings were heard and seen ninety miles
round Arquepa, and it was so dark whilst the showers of
ashes and sand lasted, that the inhabitants were obliged to
burn candles at mid-day. §

* Sir William Hamilton's Observations on Vesuvius, p. 128.

f Dr. Hooke's Post. p. 306.

J Varenius's Geography, vol. i. p. 150.

§ Dr. Hooke's Post. p. 304.

96 NATURAL CHANGES OF THE EARTH, Parti.

11. On the 16th of June, 1628, there was so terrible
an earthquake in the island of St. Michael, one of the
Azores, that the sea near it opened, and in one place
where it was one hundred and sixty fathoms deep, threw
up an island ; which in fifteen days was three leagues
long, a league and a half broad, and 3.60 feet above the
water.*

12. In the year 1631 vast quantities of boiling water
flowed from the crater of Vesuvius previous to an eruption
of fire; the violence of the flood swept away several towns
and villages, and some thousands of inhabitants.f

13. In the year 1632, rocks were thrown to the distance
of three miles from Vesuvius.^

14. In the year 1646, many of those vast mountains the
Andes § were quite swallowed up and lost. |j

15. In the year 1692, a great part of Port Royal in
Jamaica was sunk by an earthquake, and remains covered
with water several fathoms deep ; some mountains along
the rivers were joined together, and a plantation was
removed half a mile from the place where it formerly
stood. ^[

16. On the llth of January, 1693, a great earthquake
happened in Sicily, and chiefly about Catania ; the vio-
lent shaking of the earth threatened the whole island with
entire desolation. The earth opened in several places in
very long clefts, some three or four inches broad, others
like great gulfs. Not less than 59,969 persons were de-
stroyed by the falling of houses in different parts of
Sicily.**

17. In the year 1699, seven hills were sunk by an earth-
quake in the island of Java, near the head of the great
Batavian river, and nine more were also sunk near the <

* Sir W. Hamilton's Observations on Vesuvius and JEtna, p. 159.
f Ibid.

j Baddam's Abridg. Phil. Trans, vol. ii. p. 417.
§ M. Condamine represents these mountains and the Apennines
as chains of volcanoes. See his Tour through Italy, 1755.
|| Dr. Hooke's Post. p. 306.
^ Lowthorp's Abridg. Phil. Trans, vol. ii. p. 417.
** Ibid. vol. ii. p. 408, 409.

Chap. VII. BY MOUNTAINS, FLOODS, &C. 9?

Tangarang river. Between the Batavian and Tangarang
rivers, the land was rent and divided asunder, with great
clefts more than a foot wide.*

18. On the 20th of November, 1720, a subterraneous
fire burst out of the sea near Tercera, one of the Azores,
which threw up such a vast quantity of stones, &c. in the
space of thirty days, as formed an island about two
leagues in diameter and nearly circular. Prodigious
quantities of pumice stone, and half-broiled fish, were
found floating on the sea for many leagues round the
island, j-

19. In the year 1746, Callao, a considerable garrison
town and sea-port in Peru, containing 5000 inhabitants,
was violently shaken by an earthquake on the 28th of
October ; and the people had no sooner begun to recover
from the terror occasioned by the dreadful convulsion,
than the sea rolled in upon them in mountainous waves»
and destroyed the whole town. The elevation of this
extraordinary tide was such as conveyed ships of
burden over the garrison walls, the towers, and the town.
The town was rased to the ground, and so completely
covered with sand, gravel, &c. that not a vestige of it
remained. J

20. Previous to an eruption of Vesuvius, the earth
trembles, and subterraneous explosions are heard ; the
sea likewise retires from the adjacent shore, till the moun-
tain is burst open, then returns with impetuosity and
overflows its usual boundary. These undulations of the
sea are not peculiar to Vesuvius ; the earthquake which
destroyed Lisbon on the first of November 1755, was
preceded by a rumbling noise, which increased to such a
degree as to equal the explosion of the loudest cannon.
About an hour after these shocks, the sea was observed
from the high grounds to come rushing towards the city
like a torrent, though against wind and tide ; it rose forty
feet higher than was ever known, and suddenly subsided.

* Lowthorp's Abridg. Phil. Trans, vol. ii. p. 419.
f Eames's Abridg. Phil. Trans, vol. vi. part ii. page 203.
j In 1842 Hayti (St. Domingo) was visited by an earthquake that
destroyed ten thousand of its inhabitants.

98 NATURAL CHANGES OF THE EARTH, Part I.

At Rotterdam, the branches or chandeliers in a church
were observed to oscillate like a pendulum ; and we are
told it is no uncommon thing to see the surface of the
earth undulate as the waves of the sea at the time of these
dreadful convulsions of nature.*

21. The greatest eruption of Vesuvius happened in July,
1794?f , being the most violent and destructive of any men-

* The earthquake which desolated Calabria in the year 1783 was
fatal to 40,000 persons, who were crushed in the ruins, engulfed in
the earth, or burnt by the fires, besides at least 20,000 more who pe-
rished from the subsequent effects of this awful visitation. The shocks
began on the 5th of February, and continued at intervals, with different
degrees of violence, for more than three months. It destroyed the
towns and villages occupying a circuit of nearly 50 miles in diameter,
lying between 38 and 39 degrees of latitude, and extending almost
from the western to the eastern coast of the southernmost part of Italy,
besides doing considerable damage to places more remote from its
origin, which is supposed to have been either immediately under the
town of Oppido, or under some part of the sea between the west of
Italy and the volcanic island of Stromboli. Both this island and
Mount Etna exhibited appearances of eruption during the continuance
of this scene of extensive devastation, previous to which neither of
them had smoked so much as usual.

f Several eruptions of Mount Vesuvius have occurred during the
present century, some of the principal effects of which have been to
produce considerable changes in and about the crater. In an eruption
which commenced on the 22d and terminated on the 26th of De-
cember, 1817, two or three small conical hillocks, the one of which
stood near the eastern edge, and the other upon the western ridge, of
the crater, were entirely swallowed up, and the recent lava disposed
itself in the manner of a wall, fortifying, as it were, the ancient crater
upon the eastern and western sides ; convex and very irregular upon
the north and south. Of this wail, the whole of which was extremely
hot, and apparently incandescent in the interior, some parts were quite
even and regular. Upon the south, a very gently inclined plane was
produced, covered with fine sand ; the former edge of the crater about
this part having been entirely destroyed.

By the eruption of 1822 very great changes were again effected in
the crater of this mountain, which, for a century past, had been gra-
dually filling up by lava boiling up from beneath, as well as by scoria
falling from the explosions of smaller mouths, which were formed at
intervals on its base and sides, thus giving it something of the appear-
ance of an enclosed rocky plain, covered with blocks of lava and cinders,
and traversed by numerous fissures, from which clouds of vapour were
continually rising. By the violent explosions which took place during
this eruption, which began in October, and lasted upwards of twenty

Chap. VII. BY MOUNTAINS, FLOODS, &C. 99

tioned in history, except those in 79 and 1631. The lava
covered and totally destroyed 5000 acres of rich vineyards
and cultivated lands; and overwhelmed the town of
Torre-del-Greco: the inhabitants, amounting to 18,000,
fortunately escaped ; and the town is now rebuilding on
the lava that covers their former habitations. By this
eruption the top of the mountain fell in, and the mouth
of Vesuvius is now little short of two miles in circum-
ference.

Earthquakes are generally supposed to be caused by
nitrous and sulphureous vapours, enclosed in the bowels of
the earth, which by some accident take fire where there
is little or no vent. These vapours may take fire by fer-
mentation, or by the accidental falling of rocks and
stones in hollow places of the earth, and striking against
each other. When the matters which form subterraneous
fires ferment, heat, and inflame, the fire makes an effort
on every side, and if it does not find a natural vent, it
raises the earth and forms a passage by throwing it up,
producing a volcano. If the quantity of substances which
take fire be not considerable, an earthquake may ensue
without a volcano being formed. The air produced and
rarefied by the subterraneous fire may also find small
vents by which it may escape, and in this case there will
only be a shock, without any eruption or volcano. Again,
all inflammable substances, capable of explosion, produce,
by inflammation, a great quantity of air and vapour, and
such air will necessarily be in a state of very great rare-
faction : when it is compressed in a small space, like that
of a cavern, it will not shake the earth immediately above,
but will search for passages in order to make its escape,

days, the whole of this accumulated mass was entirely broken up and
thrown out, leaving an immense chasm of an irregular shape, some-
what elliptical, about three miles in circumference. Eruptions oc-
curred in the years 1828, 1831, and 1832. In the morning of Jan.
1st, 1839, Vesuvius burst forth with an explosion like the report of a
cannon, and a dense cloud of smoke and ashes soon covered Naples.
In the evening of the 2d, the mountain was on fire, and the lava
flowed down between Portici and Torre del Greco, committing great
ravages.

F 2

100 NATURAL CHANGES OF THE EARTH. Parti.

and will proceed through the several interstices between
the different strata, or through any channel or cavern
which may afford it a passage. This subterraneous air
or vapour will produce in its passage a noise and motion
proportionable to its force and the resistance it meets
with : these effects will continue till it finds a vent, perhaps
in the sea, or till it has diminished its force by expansion.

Fire, and water converted into steam, have also been
supposed principal agents in producing these phenomena.

It is evident that there is a great quantity of steam
generated in the earth, especially in the neighbourhood
of volcanoes, from the frequent eruptions of boiling
water and steam in various parts of the world. Dr.
Uno Von Troil, in his Letters on Iceland, has recorded
many curious instances. " One sees here," says he,
" within the circumference of half a mile, or three English
" miles, forty or fifty boiling springs together ; in some
" the water is perfectly clear, in others thick and clayey ;
" in some, where it passes through a fine ochre, it is tinged
'•' red as scarlet ; and in others, where it flows over a paler
" clay, it is white as milk." The water spouts up from
some of these springs continually, from others only at
intervals. The aperture through which the water rose in
the largest spring was nineteen feet in diameter, and the
greatest height to which it threw a column of water was
ninety-two feet. Previous to this eruption, a subterra-
neous noise was frequently heard, like the explosion of
cannon ; and several stones, which were thrown into the
aperture during the eruption, returned with the spouting
•water. *

* The shocks of earthquakes and the eruptions of volcanoes have
been mostly considered as modifications of the effects of one common
cause, and were usually ascribed to chemical changes going on below
the surface of the earth. The agency of the electric fluid in the pro-
duction of these phenomena is, however, now pretty generally ad-
mitted ; yet it should seem, that, notwithstanding the various hypotheses
which have been offered to account for them, the particular solution
of these phenomena is still wanting, and is, we think, likely to remain
among the desiderata of science ; since, from the numerous observ-
ations and experiments hitherto made to ascertain the cause of these
terrific, yet grand operations of nature, it seems highly probable that
they may, at various times and under peculiar circumstances, result

Chap. VIII. OF THE ATMOSPHERE, &C. 101

CHAPTER VIII.
Of the Atmosphere, Air, Winds, and Hurricanes.

THE earth is surrounded by a thin fluid mass of matter,
called the atmosphere : this matter gravitates towards the
earth, revolves with it in its diurnal motion, and goes
round the sun with it every year. Were it not for the
atmosphere, which abounds with particles capable of
reflecting light in all directions, only that part of the
heavens would appear bright in which the sun is situated,
and the stars and planets would be visible at mid-day*, buv
by means of an atmosphere, we enjoy the sun's ligh
(reflected from the aerial particles contained in the atmo-
sphere) for some time before he rises and after he sets ;
for, on the 21st of June at London, the APPARENT
day is 9 min. 16 sec. longer than the astronomical
day. This invisible fluid extends to an unknown
height ; but if, as astronomers generally estimate, the sun
begins to enlighten the atmosphere in the morning
when he comes within eighteen degrees of the horizon of

from one or other, or even from the united agency of several of those
causes to which different philosophers have individually attributed
them ; nor can we admit that it has been by any means satisfactorily
demonstrated, that the generating principle of extensive earthquakes
and volcanic eruptions are identical. The former seem, indeed, to
depend more particularly upon the accumulation of electric matter in
the bowels of the earth, while the latter may, perhaps more probably,
be supposed to originate in those causes already cited by Mr. Keith.
Those comparatively slight earthquakes which are frequently felt in
the neighbourhood of volcanoes are obviously owing to the efforts of
the burning matter to discharge itself, and they very seldom extend to
any considerable distance from the burning mountain. — ED.

* M. de Saussure, when on the top of Mont Blanc, which is
elevated 5101 yards above the level of the sea, and where consequently
the atmosphere must be more rare than ours, says that the moon shone
with the brightest splendour in the midst of a sky as black as ebony ;
while Jupiter, rayed like the sun, rose from behind the mountains in
the east. Append- voL 74. Monthly Review*
F 3

102 OF THE ATMOSPHERE, &C. Part I.

any place, and ceases to enlighten it when he is again
depressed more than 18 degrees below the horizon in the
evening, the height of the atmosphere may easily be cal-
culated to be nearly 50 miles.* Notwithstanding this
great height of the atmosphere it is seldom sufficiently
dense at two miles high to bear up the clouds ; it becomes
more thin and rare the higher we ascend. This fluid
body is extremely light, being, at a mean density, 815
times lighter than water f ; it is likewise very elastic, as
the least motion excited in it is propagated to a great
distance : it is invisible, for we are only sensible of its
existence from the effects it produces. It is capable of
being compressed into a much less space than what it
naturally possesses, though it cannot be congealed or
fixed as other fluids may ; for no degree of cold has ever
been able to destroy its fluidity. It is of different density
in every part upwards from the earth's surface, decreas-
ing in its weight the higher it rises, and consequently
must also decrease in density. The weight or pressure
of the atmosphere upon any portion of the earth's sur-
face is equal to the weight of a column of mercury which
will cover the same surface, and whose height is from
28 to 31 inches : this is proved by experiment on the
barometer, which seldom exceeds the limits above men-
tioned. Now, if we estimate the diameter of the earth

* Let A r B (Plate III. Fig. 5.) represent the horizon of an observer
at A ; s r a ray of light falling upon the atmosphere at r, and making
an angle s r B of 18 degrees with the horizon (the sun being supposed
to have that depression) the angle srA will then be. 162 degrees.
From the centre o of the earth draw o r, and it will be perpendicular
to the reflecting particles at r ; and, by the principles of optics, it will
likewise bisect the angle srA. In the right-angled triangle o A r,
the angle orA = 81°, AO = 3982 miles, the radius of the earth.
Hence, by trigonometry,

Sine of or A, 81° 9-9946199

Is to A o, 3982 3-6001013

As radius, sine of 90° 10 '0000000

Is to or 4031-76 3-6054814

*ow. if from or = 4031-6, there be taken o v = OA = 3982, the
remainder v r = 49'6 miles is the height of the atmosphere,
f .brandes Manual of Chemistry, p. 440. Edition 1841.

Chap. VIII. OF THE ATMOSPHERE, &c. 103

at 7964 * miles, the mean height of the barometer at
29| inches, and a cubic foot of mercury to weigh 13500
ounces avoirdupois, the whole weight of the atmosphere
will be 11 5222 1 14-94-20 1773089 Ibs. avoirdupois, and its
pressure upon a square inch of the earth's surface
14flbs.

The atmosphere is the common receptacle of all the
effluvia or vapours arising from different bodies, viz. of
the steam or smoke of things melted or burnt ; of the
fogs or vapours proceeding from damp, watery places ;
of steams arising from the perspiration of whatever enjoys
animal or vegetable life, and of their putrescence when
deprived of it ; also of the effluvia proceeding from
sulphureous, nitrous, acid, and alkaline bodies, &c.
which ascend to greater or less heights according to
their specific gravity. Hence the difficulty of determin-
ing the true composition of the atmosphere. Chemical
writersf , however, have endeavoured to shew that it
consists chiefly of three distinct elastic fluids, united
together by chemical affinity; namely, air, vapour, or
water, and carbonic acid gas J ; differing in their pro-

* The diameter of the earth in inches will be 504599040 ; and the
diameter with the atmosphere 504599099 inches, the difference
between the cubes of these diameters multiplied by "5236 gives
2359748914012523 1287'3564 cubic inches in the atmosphere. Now,
if 1728 cubic inches weigh 13500 ounces, as stated by Dr. Thomson,
page 6. vol. iv. of his Chemistry, the weight of the atmosphere will be
determined as above. If the square of the diameter 5O4599040 be
multiplied by 3 '14 16, the product will give the superficies of the
earth, =799914792576284098-56 square inches; and if the weight
of the atmosphere be divided by this superficies, the quotient will be
14-4lbs. = 14flbs. the pressure of the atmosphere on every square inch
of the earth's surface. The pressure of the atmosphere on a square
inch of surface, may likewise be found by experiments made with
the air-pump, or by weighing a column of mercury whose base is one
inch square, and height 29^ inches.

f Dr. Thomson's Chemistry, page 34. vol. iv. edition of 1810.

j Gas is a term applied by chemists to all permanently elastic
fluids, except common air ; and carbonic acid gas is what was for-
merly called fixed air, or such as extinguishes flame, and destroys
animal life.

F 4

104? OF THE ATMOSPHERE, &C. Part I.

portions at different times and in different places ; but
the average proportion of each, supposing the whole
atmosphere to be divided into 100 equal parts, is given
bv Dr. Thomson as follows :
98 & air,

1 vapour or water,
^ carbonic acid.

100

Hence it appears, that the foreign bodies which are
mixed or united with the air in the atmosphere are so
minute in quantity, when compared with it, that they
have no very sensible influence on its general properties ;
wherefore, in describing the mechanical properties of
the air, in the succeeding parts of this chapter, no at-
tention is paid to its component parts in a chemical point
of view ; but wherever the word air occurs, common or
atmospheric air is always meant. It may, however, be
proper to remark here, that from various * experiments :
chemists have inferred that if atmospheric air be divided
into 100 parts, 21 of those parts will be vital air, and 79
poisonous; hence the vital air does not compose one-
third of the atmosphere.

Air is not only the support of animal and vegetable
life, but it is the vehicle of sound ; and this arises from
its elasticity : for a body being struck vibrates, and com-
municates a tremulous motion to the air ; this motion
acts upon the cartilaginous portion of the ear, where
there are several eminences and concavities adapted to
convey it into the auditory passage, where it strikes on

* Without reference to foreign matter, modern chemists find, on
an average of results, that the ordinary constituents of the atmosphere
are in the following proportions : -
By measure. By weight.

77-50 75-55 Nitrogen or Azotic gas (poisonous).

21 -00 23-32 Oxygen gas (vital air).

1 '42 1 -03 Aqueous vapour.

0'08 O'lO Carbonic acid.

100-00 100-00 Branded Chemistry, p. 451.

Chap. VIII. OF THE ATMOSPHERE, &C. 105

the membrana tympani, or drum of the ear, and produces
the sense of hearing.

From the fluid state of the atmosphere, its great sub-
tilty and elasticity, it is susceptible of the smallest
motion that can be excited in it ; hence it is subject to
the disturbing forces of the moon and the sun ; and tides
will be generated in the atmosphere similar to the tides
in the ocean. By the continual motion of the air, noxious
vapours, which are destructive to health, are in some
measure dispersed ; 'so that the air, like the sea, is kept
from putrefaction by winds and tides.

Air may be vitiated, by remaining closely pent up in
any place for a considerable length of time ; and when
it has lost its vivifying spirit, it is called carbonic acid,
choke-damp, or fixed air, not only because it is filled
with humid or moist vapours, but because it deadens fire,
extinguishes flame, and destroys life.

If part of the vivifying spirit of air in any country
begins to putrefy, the inhabitants of that country will
be subject to an epidemical disease, which will con-
tinue until the putrefaction is over : and as the putrefying
spirit occasions this disease, so, if the diseased body
contribute towards the putrefying of the air, then the
disease will not only be epidemical, but pestilential and
contagious.

The air will press upon the surfaces of all fluids, with
any force, without passing through them or entering into
them; so that the softest bodies sustain this pressure
without suffering any change in their figure, and the
most brittle bodies bear it without being broken. Thus
the weight of the atmosphere presses upon the surface
of water, and forces it up into the barrel of a pump. It
likewise keeps mercury suspended at such a height,
that its weight is equal to the pressure, and yet it
never forces itself through the mercury into the vacuum
above.

Another property of tbe air is, that it is expanded by
heat, and condensed or contracted by cold : hence the
fire rarefying the air in the chimneys, causes it to ascend
the funnels ; while the air in the room, by the pressure of
the atmosphere, is forced to supply the vacancy, and

*106 OF THE ATMOSPHERE, &C. Part I.

rushes into the chimney in a constant torrent, bearing
the smoke into the higher regions of the atmosphere.
In large cities, in the winter, where there are many
.fires, people, and animals, the air is considerably more
rarefied than in the adjoining country ; for which reason,
continual currents of colder air rush in at all the ex-
terior streets, bearing up the attenuated and conta-
minated air above the tops of the houses and the highest
buildings, and supplying their place with air of a more
salubrious quality. The more extensive winds owe their
origin to the heat of the sun ; this heat acting upon some
part of the air causes it to expand, and become lighter,
and consequently it must ascend ; while the air adjoin-
ing, which is more dense and heavy, will press forward
towards the place where it is rarefied. Upon this prin-
ciple, we can easily account for the trade-winds, which
blow constantly from east to west about the equator;
for when the sun shines perpendicularly on any part
of the earth, it will heat and rarefy the air in that part,
and cause it to ascend ; while the adjacent air will rush
in to supply its place, and consequently will cause a
stream or current of air to flow from all parts towards
that which is the most heated by the sun. But as the
sun, with respect to the earth, moves from east to west,
the common course of the air will be from east to west :
and therefore at or near the equator, where the mean
heat of the earth is the greatest, the wind will blow
continually from the east; but on the north side of
the equator it will decline a little to the north ; and,
on the south side of the equator it will decline to the
south. If the earth were covered with water, the
motion of the wind would follow the apparent motion
of the sun, in the same manner as the motion of the
water would follow the motion of the moon ; but, as the
regular course of the tides is changed by the obstruc-
tion of continents, islands, &c. so the regular course
of the winds is changed by high mountains, by the
declination of the sun towards the north and south, by
burning sands which retain the solar heat to an incre-
dible degree, by the falling of great quantities of rain,
which causes a sudden condensation or contraction of

Chap. VIII. OF THE ATMOSPHERE, &C. 107

the air, by exhalations that rise out of the earth at certain
times and places, and from various other causes. Thus,
according to Dr. Halley, between the 3d and 10th degree
of south latitude, the south-east trade-wind continues
from April to October ; during the rest of the year the
wind blows from the north-west ; but between Sumatra
and New Holland this monsoon * blows from the south
during our summer months ; it changes about the end of
September, and continues in the opposite direction till
April.

Over the whole of the Indian Ocean, to the northward
of the third degree of south latitude, the north-east
trade-wind blows from October to April, and a south-west
wind from April to October.f From Borneo, along the
coast of Malacca, and as far as China, this monsoon in
our summer blows nearly from the south, and in the
winter from north by east. Near the coast of Africa,
between Mosambique and Cape Guardafui, the winds are
irregular during the whole year, owing to the different
monsoons which surround that particular place. Mon-
soons are likewise regular in the Red Sea ; between
April and October they blow from the north-west, and
during the other months from the south-east, keeping
constantly parallel to the Arabian coast.J

On the coast of Brazil, between Cape St. Augustine
and the island of St. Catherine, from September to
April the wind blows from the east or north-east; and
from April to September it blows from the south-west;
so that monsoons are not altogether confined to the Indian
Ocean.

On the coast of Africa, from Cape Bajador, opposite
to the Canary Islands, to Cape Verd, the winds are gene-
rally north-west ; and from hence to the island of St.

* The regular winds in the Indian seas are called monsoons, from
the Malay word moosin, which signifies " a season." Forest's Voyage,
page 95.

f The student will find these winds represented on Adams' globes,
by arrows having the barbed points flying in the direction of the wind,
as if shot from a bow ; and, where the winds are variable, these arrows
seem to be flying in all directions.

\ Bruce's Travels, vol. i. chap. iv.
F 6

108 OF THE ATMOSPHERE, &C. Part I.

Thomas, near the equator, they blow almost perpendicu-
lar to the shore.

In all maritime countries of any considerable extent,
between the tropics, the wind blows during a certain
number of hours from the sea, and during a certain
number from the land; these winds are called sea and
land breezes. During the day, the air above the land
is hotter and more rare than that above the sea; the
sea air therefore flows in upon the land, and supplies the
place of the rarefied air, which is made to float higher in
the atmosphere ; as the sun descends, the rarefaction of
the land air is diminished, and an equilibrium is restored.
As the night approaches, the denser air of the hills and
mountains (for where there are no hills, there are no
sea and land breezes) falls down upon the plains, and
pressing upon the air of the sea, which has now become
comparatively lighter than the land air, causes the land
breeze.

The Cape of Good Hope is famous for its tempests,
and the singular cloud which produces them : this cloud
appears at first only like a small round spot in the sky,
called by the sailors the Ox's Eye, and which probably
appears so minute from its exceedingly great height.

In Natolia, a small cloud is often seen, resembling
that at the Cape of Good Hope, and from this cloud a
terrible wind* issues, which produces similar effects. In
the sea between Africa and America, especially at the
equator and in the neighbouring parts, tempests of this
kind very often arise, and are generally announced by
small black clouds. The first blast which proceeds from
these clouds is furious, and would sink ships in the open
sea, if the sailors did not take the precaution to furl their
sails. Ihese tempests seem to arise from a sudden rare-
faction of the air, which produces a kind of vacuum, and
the cold dense air rushing in to supply the place.

Hurricanes, which arise from similar causes, have a

whirling motion which nothing can resist. A calm ge-

ally precedes these horrible tempests, and the sea then

rf L1^ W1!nd,seems to *e Ascribed by St. Paul, in the 27th chapter
of the Acts, by the name of the Euroclydo.

Chap. VIII. OF THE ATMOSPHERE, &C.

109

appears like a piece of glass ; but, in an instant, the fury
of the winds raises the waves to an enormous height.
When from a sudden rarefaction, or any other cause,
contrary currents of air meet in the same point, a whirl-
wind is produced.

The force of the wind upon a square foot of surface is
nearly as the square of the velocity ; that is, if on a
square board of one foot in surface, exposed to a wind,
there be a pressure of one pound, another wind, with
double the velocity, will press the board with a force of
four pounds, &c. The following table, extracted from the
Philosophical Transactions, shews the velocity and pres-
sure of the winds, according to their different appellations.

Velocity of the wind.

Perpendicular
ibrce on one
square foot in
Dounds avoir-
dupois.

Common appellations of
the winds.

Miles in
one hour.

Feet in one
second.

1-47

•005

Hardly perceptible.

2^
3

2-93)
4-4-0 j

•020)
•044 j

Just perceptible.

4'
5

5-877
7-33 \

•079)
•123 J

Gentle pleasant wind.

io:

•

14-67 f
22-00 ]

•4927
1-107 j

Pleasant brisk gale.

20-
25

•

29-34 }
36-67 3

l-968\
3-075 j

Very brisk.

30]
35

44-01 1
51-34J

4-429 1
6-027 j

High winds.

40-
45

58.68 I
66-01 J

7-873 I
9.963 j

Very high.

so"

73-35

12-300

A storm or tempest.

88-02

17-715

A great storm.

117-36

31-490

A hurricane.

rA hurricane that

100

146-70

49-200

J tears up trees, and
J carries buildings,

\&c. before it.

110

CHAPTER IX.

Of Vapours, Fogs and Mists, Clouds, Dew and Hoar Frost,
Rain, Snow and Hail, Thunder and Lightning, Falling
Stars, Ignis Fatifus, Aurora Borealis, and the Rainbow.

1. Vapours are composed of aqueous or watery par-
ticles, separated from the surface of the water or moist
earth by the action of the sun's heat ; whereby they are
so rarefied and separated from each other, as to become
specifically lighter than the air, and consequently they
rise and float in the atmosphere.

2. FOGS AND MISTS. Fogs are a collection of vapours
which chiefly rise from fenny moist places, and become
more visible as the light of the day decreases. If these
vapours be not dispersed, but unite with those that rise
from water, as from rivers, lakes, &c., so as to fill the air
in general, they are called mists.

3. CLOUDS are generally supposed to consist of va-
pours exhaled from the sea and land.* These vapours
ascend till they are of the same specific gravity as the
surrounding air ; here they coalesce, and by their union
become more dense and weighty. The more thin and
rare the clouds are, the higher they soar ; but their height
seldom, if ever, exceeds two miles. The generality of
clouds are suspended at the height of about a mile ;

* Dr. Thomson, in vol. iv. of his Chemistry, page 79, &c. edition
of 1810, says, it is remarkable that, though the greatest quantity of
vapours exists in the lower strata of the atmosphere, clouds never
begin to form there, but always at some considerable height. The heat
of the clouds is sometimes greater than that of the surrounding air.
The formation of clouds and rain is neither owing to the saturation of
the atmosphere, nor the diminution of heat, nor the mixture of airs of
different temperatures. Evaporation often goes on for a month toge-
ther in hot weather, especially in the torrid zone, without any rain.
The water can neither remain in the atmosphere, nor pass through it,
in a state of vapour. What then becomes of the vapour after it enters
the atmosphere? what makes it lay aside the new form which it must
have assumed, and return again to its state of vapour, and fall down in
rain ? Till these questions are experimentally answered, Dr. Thomson
concludes, that the formation of clouds and rain cannot be accurately
accounted for.

Chap. IX. OF VAPOURS, FOGS, CLOUDS, &c. Ill

sometimes, when the clouds are highly electrified, their
height is not above seven or eight hundred yards. The
wonderful variety in the colours of the clouds is owing to
their particular situation to the sun, and the different re-
flections of his light. The various figure of the clouds
probably proceeds from their loose and voluble texture,
revolving in any form, according to the different force of
the winds, or from the electricity contained in them.

" The general colour of the sky is blue, and this is oc-
casioned by the vapours which are always mixed with air,
and which have the property of reflecting the blue rays,
more copiously than any other." — Saussure.

4. DEW. When the earth has been heated in the day-time
by the sun, it will during the night throw off a portion of
the heat it has so acquired. " The extent to which the
diminution of temperature takes place depends greatly
upon the aspect of the sky : on a clear night it goes on
more rapidly, and to a much greater extent, than when
the sky is overcast or cloudy, hence in clear nights there
is a much greater deposition of dew than in cloudy
weather. To understand this, it must be recollected, that
dew is not a kind of fine rain showering down upon the
earth from above, but that it depends upon the deposition
of moisture from the atmosphere, and is, in its formation,
precisely similar to what happens when a glass of iced
water is brought into a warm room in summer; the cold-
ness of its surface abstracts the heat from the vapour in
the air and causes its condensation in the form of water,
which is deposited exactly like dew upon the outside of
the vessel." When dew freezes it produces hoar-frost.

5. RAIN. When the weight of the air is diminished,
its density will likewise be diminished, and consequently
the vapours that float in it will be less resisted, and begin
to fall, and, as they begin to strike upon one another in
falling they will unite and form small drops. But when
the small drops of which a cloud consisted are united
into such large drops, that no part of the atmosphere is
sufficiently dense to produce a resistance able to support
them, they will then fall to the earth, and constitute what
we call rain. If these drops be formed in the higher
regions of the atmosphere, many of them will be united

112 OF VAPOURS, FOGS, CLOUDS, &c. Part

before they come to the ground, and the drops of rain
will be very large. * The drops of rain increase so much
both in bulk and motion, during their descent, that a
bowl placed on the ground would receive, in a shower of
rain, almost twice the quantity of water that a similar
bowl would receive on a neighbouring high f steeple.
The mean annual quantity of rain is greatest at the equa-
tor, and decreases gradually as we approach the poles.

Thus, at

Latitude. Depth of rain.

J Grenada, West Indies, - 12° 0' - 126 inches.

St. Domingo, Cape St. Francois 19° 46' - 120

Calcutta - - - 22' 23' - 81

In England - - 53° 0' - 35

Petersburgh - - 59° 16' - 16

On the contrary, the number of rainy days is smallest
at the equator, and increases in proportion to the distance
from it. The number of rainy days, is often greater in
winter than in summer : but the quantity of rain is greater
in summer than in winter. More rain falls in mountainous
countries than in plains. Among the Andes, it is said
to rain almost perpetually, while in the plains of Peru
and in Egypt, it hardly ever rains at all. The mean
annual quantity of rain for the whole globe is estimated
by Dr. Thomson at 34- inches in depth : hence may be
found the whole quantity of rain that falls in a year upon
the whole surface of the earth and sea, in the same man-
ner as the number of cubic inches were found in the
atmosphere, in Chapter VIII. of this work. The same
author observes that, for every square inch of the earth's
surface, about 41 cubic inches of water is annually evapo-
rated ; so that the average quantity of rain is considerably
less than the average quantity of water evaporated.

* Dr. Rutherford's Natural Philosophy, vol. ii. chap. 10. Signior
Beccaria, whose observations on the general state of electricity in the
atmosphere have been very accurate and extensive, ascribes the cause
of rain, hail, snow, &c. &c. to the effect of a moderate electricity in
the atmosphere.

f Mr. Adam Walker's Familiar Philosophy, lect. v. page 215.

\ Dr. Thomson's Chemistry, vol. iv. page 83, &c. edition of 1810.

Chap. IX. OF VAPOURS, FOGS, CLOUDS, &c. 113

6. SNOW AND HAIL. Snow consists of such vapours
as are frozen while the particles are small ; for, if these
stick together after they are frozen, the mass that is form-
ed out of them will be of a loose texture, and form little
flakes or fleeces, of a white substance, somewhat heavier
than the air, and therefore will descend in a slow and
gentle manner through it. Hail, which is a more com-
pact mass of frozen water, consists of such vapours as are
united into drops, and are frozen while they are * falling.

7. THUNDER AND LIGHTNING. It has been already
observed, that the atmosphere is the common receptacle
of all the effluvia, or vapours, arising from different bodies.
Now, when the effluvia of sulphureous and nitrous f bodies
meet each other in the air, there will be a strong conflict,
or fermentation between them, which will sometimes be
so great as to produce fire.J Then, if the effluvia be
combustible, the fire will run from one part to another,
just as the inflammable matter happens to lie. If the in-
flammable matter be thin and light, it will rise to the
upper part of the atmosphere, where it will flash without
doing any harm ; but if it be dense, it will lie near the
surface of the earth, where, taking fire, it will explode
with a surprising force, and by its heat rarefy and drive
away the air, kill men and cattle, split trees, walls, rocks,
&c. and be accompanied with terrible claps of thunder.
The effects of thunder and lightning are owing to the sud-
den and violent agitation the air is put into, together with
the force of the explosion. Stones and bricks struck by
lightning, are often found in a vitrified state. Signior
Beccaria supposes that some stones in the earth, having
been struck in this manner, gave rise to the vulgar opinion
of the thunder-bolt. It is now generally admitted that
lightning and the electrical fluid are the same.}

* Rutherford's Philosophy, vol. ii. chap. 10.

t Gunpowder, the effects of which are similar to thunder and light-
ning, is composed of six parts of nitre, one part of sulphur, and one
part of charcoal.

J Professor Winkler's Philosophy.

§ Signior Beccaria, of Turin, observes that the atmosphere abounds
with electricity ; and if a cloud which is positively charged (viz.
which has more than its natural share of electrical fluid) pass near
another cloud which is negatively charged (viz. which has less than its

114- OF VAPOURS, FOGS, CLOUDS, &C. Parti.

8. FALLING STARS and other fiery meteors, the origin
and nature of which appear to be involved in great obscurity,
have of late years excited extraordinary interest, in conse-
quence of their periodical appearance, in vast numbers,
generally about the 10th of August and the 12th and 13th
of November. The heights at which they move have been
estimated at from 10 to 460 miles, and their velocities at
from 10 to 36 miles in a second. Respecting their nature
little seems yet to be known ; for whilst some eminent phi-
losophers and astronomers have supposed them to be gene-
rated in the atmosphere, others have imagined that they
were projected from the moon : the prevailing opinion of
astronomers now is, that they belong to the solar system,
and accompany the earth in its orbit.

The disappearance of fiery meteors is frequently accom-
panied by a loud explosion like a clap of thunder, and
heavy stony bodies have been observed to fall from them
to the earth. Dr. Thomson has given a table of 36
showers of stones, with the places where they fell, the
dates, and the testimonies annexed. *

These stony bodies, when found, are always hot, and
their size differs from a few ounces to several tons. They
are usually round, and always covered with a black crust.
When broken, they appear of an ash-grey colour, and of
a granular texture, like coarse sandstone. These sub-
stances are probably concretions actually formed in the
atmosphere, but in what manner no rational account has
yet been given.

9. OF THE IGNIS FATUUS, commonly called Will-
with-a- Wisp, or Jack-with-a- Lantern. This meteor, like
most others, has not failed to attract the attention of
philosophical inquirers. Sir Isaac Newton, in his Optical
Queries, calls it a vapour shining without heat. Various
accounts of it may be seen in the Philosophical Trans-
actions. The most probable opinion is, that it consists

natural share of electrical fluid), they will attract each other, and a
quick deprivation of the electrical fluid will take place : the flash is
called lightning, the report thunder (the ensuing rollings are only
echoes from distant clouds).

* In the Edinburgh Philosophical Journal for 1819, is given an
« account of meteoric stones, masses of iron, showers of dust, red snow,
&c., which have fallen from the earliest period down to 1819."

Chap. IX. OF THE AURORA BOREALIS. 115

of inflammable air *, or oleaginous matter, emitted from
a putrefaction and decomposition of vegetable substances,
in marshy grounds ; which being kindled by some electric
spark or other cause unknown to us, will continue to burn
or reflect a kind of thin flame in the dark, without any
sensible degree of heat, till the matter which composes
the vapour is consumed. This meteor never appears on
elevated grounds, because they do not sufficiently abound
with moisture to produce the inflammable air, which is
supposed to issue from bogs and marshy places. It is
often observed flying by the sides of hedges, or following
the course of rivers ; the reason of which is obvious, for
the current of air is greater in these places than else-
where. These meteors are very common in Italy and in
Spain. Dr. Shaw \ has described a remarkable ignis
fatuus, which he saw in the Holy Land, when the atmo-
sphere was so uncommonly thick and hazy, that the dew
on the horses' bridles was remarkable clammy and unctu-
ous. This meteor was sometimes globular, then in the
form of the flame of a candle, presently afterwards it
spread itself so much as to involve the whole company in
a pale harmless light, and then it would contract itself
again, and suddenly disappear ; but, in less than a minute,
it would become visible as before, and running along from
one place to another with a swift progressive motion,
would again expand itself, and cover a considerable space
of ground.

10. OF THE AURORA BOREALIS, Or NORTHERN

LIGHTS. There have been various opinions and conjec-
tures respecting the cause and properties of these extra-
ordinary phenomena J ; and the most probable opinion is,
that they arise from exhalations, and are produced by a

* Inflammable air may be made thus : exhaust a receiver of the air-
pump, let the air run into it through the flame of the oil of turpentine,
then remove the cover of the receiver, and hold a lighted candle to the
sir, it will take fire, and burn quicker or slower according to the density
of the oleaginous vapour.

f Shaw's T/avels, p. 363.

\ Philosophical Transactions, No. 305. 310. 320. 347, 348, 349.
SSI, 352. 363. 365. 368. 576. 385. 395. 398, 399. 402. 410. 418.
431. and 433., &c.

116 OF THE RAINBOW. Parti.

combustion of inflammable air, caused by electricity. —
This inflammable air is generated particularly between the
tropics, by many natural operations, such as the putre-
faction of animal and vegetable substances, volcanoes, &c. ;
and being lighter than any other, ascends to the upper
regions of the atmosphere, and, by the motion of the
earth, is urged towards the poles ; for it has been proved
by experiments that whatever is lighter, or swims on
a fluid which revolves on an axis, is urged towards the
extreme points of that axis * : hence these inflammable
particles continually accumulate at the poles, and by
meeting with heterogeneous matter take fire, arid cause
those luminous appearances frequently seen towards the
polar regions, f

In high latitudes the Auroras Boreales appear with the
greatest lustre, and extend over the greater part of the
hemisphere, varying their colours from all the tints of
yellow to the most obscure russet. J In the north-east
parts of1 Siberia, Hudson's Bay, &c. they are attended by
a continued hissing and cracking noise through the air
similar to that produced by fire-works. §

11. OF THE RAINBOW. The rainbow is the most
beautiful meteor with which we are acquainted : it is never
seen but in rainy weather, where the sun illuminates the

* See Mr. Kirwan's account of the Aurora Borealis, Irish Phil.
Transactions for 1788, page 70.

f We have very few accounts of the Aurora Australia, or Southern
Lights, owing perhaps to the want of observations in those remote parts
of the globe, and a proper channel of information. Captain Cook, in
his second voyage towards the south pole, says : " (February 17th
1773,) We observed a beautiful phenomenon in the heavens, consisting
of long columns of clear white light, shooting up from the heavens to
the eastward, almost to the zenith, and gradually spreading over the
whole southern part of the sky. Though these columns were in most
respects similar to the Aurora Borealis, yet they seemed to differ from
them in being always of a whitish colour. The stars were sometimes
hid by, and sometimes faintly to be seen through, the substance of
these Auroras Australes. The sky was generally clear when they ap-
peared, and the air sharp and cold, the thermometer standing at the
freezing point ; the ship being in latitude 58° south."

| Dr. Rees's Cyclopaedia, word Aurora Borealis.

§ Philosophical Transactions, vol. Ixxiv. page 288.

Cftap. IX. OF THE RAINBOW. 117

falling rain, and when the spectator turns his back to the
sun. There are frequently two bows seen, the interior
and exterior bow. The interior bow is the brightest,
being formed by the rays of light falling on the upper
parts of the drops of rain ; for a ray of light entering the
upper part of a drop of rain will, by refraction, be thrown
upon the inner part of the spherical surface of that drop,
whence it will be reflected to the lower part of the drop,
where, undergoing a second refraction, it will be bent to-
wards the eye of the spectator ; hence the rays which fall
upon the interior bow come to the eye after two refrac-
tions and one reflection, and the colours of this bow from
the upper part are red, orange, yellow, green, blue, indigo.
and violet. The exterior bow is formed by the rays of
light falling on the lower parts of the drops of rain ; these
rays, like the former, undergo two refractions, viz. one
when they enter the drops, and another when they emerge
from the drops to the eye ; but they suffer two or more
reflections in the interior surface of the drops ; hence the
colours of these rays are not so strong and well defined as
those in the interior bow, and appear in an inverted order,
viz. from the under part they are red, orange, yellow,
green, blue, indigo, and violet. To illustrate this by ex-
periment, suspend a glass globe filled with water in the
sun-shine, turn your back to the sun, and view the globe
at such a distance that the part of it the farthest from the
sun may appear of a full red colour, then will the rays
which come from the globe to the eye make an angle of
4-2 degrees with the sun's direct rays ; and if the eye re-
main in the same position, and another person lower the
glass globe gradually, the orange, yellow, green, &c.
colours, will appear in succession, as in the interior bow.
Again, if the glass globe be elevated, so that the side
nearest to the sun may appear red, the rays which come
from the globe to the eye will make an angle of about
50 degrees : then, if another person gradually raise the
glass globe, while the spectator remains in the same posi-
tion, the rays will successively change -from red to orange,
green, yellow, &c. as in the exterior bow. These observ-
ations being understood, let d n e (Plate IV. Fig. 1.)
represent a drop of rain belonging to the interior bow,

118 OF THE RAINBOW. Part I.

s d a ray of light falling on the upper part of the drop at
d; instead of the ray continuing its direction towards F,
it will be refracted or bent towards n, whence part of it
(for some will pass through the drop) will be reflected to
e, making the angle of incidence dnk equal to the angle
of reflection enk; instead of continuing its direction from
c towards 1 it will, by emerging out of the water into the
air, be again refracted to the eye at o. But, as this ray
of light consists of a pencil* of rays, some of which are
more refrangible f than others, the violet, which is the
most refrangible, will proceed towards B, and the red,
which is the least refrangible, will proceed towards o.
Now, if the eye of the spectator be so placed that the ray
of light falling upon it has been once reflected, and twice
refracted, so that o e shall make, with the solar ray, s G?,
an angle smo of 42° 2'f, he will see the red ray in the
direction oem; and if the eye be raised to B, so that Be
shall make, with the solar ray s d, an angle B F s of 40° 17'
the violet ray will be seen in the direction B e F ; the red
ray will appear the highest, the violet the lowest, and
the rest in order according to their different refrangi-
bility, as in the interior bow (Fig. 2. Plate IV.) ; for the

* A pencil of rays is a portion of light of a conical form diverging
or proceeding from a point ; or tending to a point, in which case the
rays are said to converge.

f Refrangibility of the rays of light is their tendency to deviate from
their natural course. Those rays which deviate the most from their
natural course, in passing out of one medium into another, are said to
be the most refrangible ; and those which deviate the least from their
natural course are the least refrangible. Sir Isaac Newton, by experi-
ment, found the red rays to be the least refrangible, and the violet rays
the most ; and those rays which are the least refrangible are likewise
the least reflexible.

\ The sine of incidence and refraction of the least refrangible ray,
out of water into air, is as 3 to 4, or as 81 to 108 ; and the most re-
frangible, as 81 to 109. Emerson's Optics, p. 92. — The same author,
at page 237. prob. xxvi. of his Optics, by the method of fluxions or
increments, and using the numbers above, finds that the angle which
the emergent ray makes with the incident ray in the interior bow, is
42° 2' for the red, and 40° 17' for the violet ; and for the exterior bow,
these angles are 50° 57', and 54° 7'. The investigations are here
omitted, because they cannot be rendered intelligible to any persons but
mathematicians.

Chap. IX. OF THE RAINBOW. 1J9

drop of water descends from F to e. What has been ob-
served of one drop of water, will be true in an infinite
number of drops ; hence the interior bow is composed of
a circular arc, whose breadth F e, is proportional to the
difference between the least and most refrangible rays.

To explain the exterior bow, Let ctnd (Plate IV
Pig. 1.) represent a drop of rain, sd a ray of light falling
upon the under part of it at d; instead of this ray con-
tinuing its direction towards m, it will be refracted to n,
whence part of it will pass through the drop, and the rest
will be reflected to t; at t a part of it will again pass
through the drop, and the remainder will be reflected to
c ; then in emerging from the water into the air, instead
of continuing the direction cz, it will be refracted from c
to the eye at o. But as this ray of light, like that in the
interior bow, consists of a pencil of rays of different re-
frangibility, the red, which is the least refrangible, will
proceed towards A ; and the violet, which is the most
refrangible, will proceed towards o. Now, if the eye of
the spectator be so placed that the ray of light falling
upon it has been twice reflected, and twice refracted, so
that o o shall make with the solar ray s o an angle s o o
of 54-° 7', he will see the violet ray in the direction o c v ;
and if the eye be raised to A, so that A o shall make with
the solar ray s o an angle s o A of 50° 57', the red ray will
be seen in the direction ACT; the violet ray will appear
the highest, and the red ray the lowest, and the rest in
order according to their different refrangibility, as in the
exterior bow (Plate IV. Fig. 2.) for the drop of water
descends from H to d. The same observations apply to
an infinite number of drops, as in the interior bow.

Hence, if the sun were a point, the breadth of the ex-
terior bow would be (54-° 7' - 50° 57' =) 3° 10', that of
the interior bow (4-2° 2' - 40° 17' =) 1° 45', and the dis-
tance between them (50° 57'— 42° 2' =) 8° 55'; but, as
the mean diameter of the sun is about 32' 2", the breadths
of the bows must be increased by this quantity, and their
distances diminished; the breadth of the exterior bow
will then be 3° 42', that of the interior bow 2° IT, and
their distance 8° 23'. The greater semi-diameter of the
interior bow will be (42° 2' -t- 16", the sun's semi-diame-

120 OF THE RAINBOW. Part I.

ter =) 4-2° IS', and the least semi-diameter of the exterior
bow (50° 57' — 16' the sun's semi-diameter =) 50° 41'.

All rainbows are arcs of equal circles, and consequently
are equally large, though we do not always see an equal
quantity of them ; for the eye of a spectator is the vertex
of a cone, and its circular base is the rainbow, the semi-
diameter of which (for the interior bow) is the fixed
quantity 42° 18', equal to a angle FOP ; and as SF will
in all situations be parallel to OP, and the angle SFO, equal
to FOP, must be always equal to 42° 18', it is evident that
as s rises, F and p will sink ; and when SF makes an angle
of 42° IS' with the horizon, OF will coincide with OQ, and
the interior bow will vanish ; hence the interior bow can-
not be seen if the sun's altitude exceed 42° 18': again,
as the point P rises, the point s will sink, and when OP
coincides with OQ, SF will be parallel to the horizon, (viz.
the sun will be rising or setting,) and the whole semi-
diameter of the rainbow will appear, which is the greatest
part of it that ever can be seen on ' level ground ; hence
half a rainbow is the most that can be seen in such a situ-
ation ; but if the observer be on the top of a high moun-
tain, such as the Andes, with his back to the sun, and if
it rains in a valley before him, a whole rainbow may be
seen, forming a complete circle. The above reasoning is
equally applicable to the outer bow ; hence, as the sun
rises^ the bows sink, and when his altitude exceeds 42° 18'
the interior bow cannot be seen, and, if it exceeds
54° 7' -f- 16' =) 54° 23', the exterior bow cannot be seen.

121
PART II.

THE ELEMENTARY PRINCIPLES OP ASTRONOMY,

ASTRONOMY determines the altitudes, distances, mag-
nitudes, and orbits of the heavenly bodies ; describes
their various apparent and real motions, their periodical
revolutions, .eclipses or occultations, and furnishes us
with a rational account of the various phenomena of the
Heavens.

CHAPTER I.
The General Appearance of the Heavens.

IF, on a clear night, we stand facing the south and ob-
serve the heavens, they will appear to undergo a continual
change.* Some stars will be seen ascending from the
cask or rising ; others descending towards the west, or
setting. In some intermediate point between the east
and west, each star will reach to its greatest height, or
will culminate. The greatest heights of the several stars
will be different, but these heights will all be attained
when the stars have arrived at a point exactly half way
between the east and the west, viz. at the south.

If we now turn our backs to the south, and observe the
north, new phenomena will present themselves. Some
stars will appear as before, rising, attaining their greatest
heights and setting ; other stars will be seen, that never
set, moving with different degrees of velocity ; and some
nearly stationary.

* Exposition du Syst^me clu Monde, p. 2.
G

122 THE APPEARANCE OF THE HEAVENS. Part II.

The stars which never set appear to revolve about one
particular star, and to describe circles of greater circum-
ferences according to their distances from that star. The
stationary star is called the Polar star, and the stars
which revolve round it at small distances are called the
circumpolar stars.

The polar star which appears in the heavens is not
stationary, neither is it situated exactly in the pole, but
about a degree and three quarters from it * ; that is,
from a point in which, if a star were situated, it would

appear perfectly fixed.
The general

general appearance, therefore, of the starry
heavens is that of a vast concave sphere, turning round
two imaginary fixed points diametrically opposite to
each other, the one in the north, the other in the south,
and this apparent revolution is performed in about 24?
hours.

Almost all the stars in the heavens retain towards each
other the same relative position, they neither approach
towards, nor recede from each other, and are therefore
called fixed stars. There are, however, other celestial
bodies, having the appearance of stars, which continually
change their places ; these are called planets.

The two celestial bodies of the most interesting appear-
ance, and which claim our greatest attention, are the sun
and the moon. These vary their situations from day to
day in the heavens ; sometimes they appear in the same
point of the heavens, and at other times directly opposite
to each other.

The moon changes her figure every month, in whicli
time she makes a complete tour round the heavens ; and
though she appears to rise and set every day like the stars,
and to move from east to .west, yet her apparent motion
is retarded, and when compared with any particular fixed
star she seems to go backward or towards the east : that
is, if on any night she be seen in conjunction with a par-
ticular fixed star, the next night she will appear about
13° to the eastward of that star, the succeeding night

See the note to Def. 4. page 2.

Chap. I. THE APPEARANCE OF THE HEAVENS. 123

at the same hour she will appear 26° to the eastward of
the star, and so on.

The common phenomena of the rising and setting of
the stars, and their apparent revolution from east to west,
are easily accounted for, on the simple hypothesis of the
earth's revolution on its axis from west to east (See Part I.
Chap. IV.) ; but the continual change of place which the
sun, the moon, and the planets undergo, cannot be ac-
counted for on the same hypothesis, nor on, the supposi-
tion that the whole heavens revolve from east to west in
24> hours.

The sun apparently moves towards the stars, which set
after him, and from those which set before him : that is,
to a spectator in the northern hemisphere, facing the
south, his apparent motion is from the right hand to the
left.

The sun's apparent motion from west to east with re-
spect to the fixed stars, will adequately explain why
certain remarkable stars, and groups of stars called constel-
lations, are seen in the south at different hours of the night
during the year. For the hour depends entirely on the
sun : it is noon when he is in the south. Stars which are
directly opposite to him are, therefore, by the rotation
of the earth on its axis, brought to the meridian at mid-
night.

But the stars which are on the meridian at twelve
o'clock one night, cannot again be there at the same hour
on the succeeding night ; for the sun's place being re-
moved a little to the east, the stars which were opposite
to him before are now opposite to a part of the heavens a
little to the westward of the sun, and therefore they will
come to the meridian a little before midnight : and, on
each succeeding night, they will come to the meridian by
greater intervals before midnight ; so that, in the course
of the year they are all successively in the south, though
sometimes they are invisible on account of their nearness
to the sun.

The moon also moves among the stars from the west to-
wards the east, more rapidly than the sun appears to move :
the apparent motion of the sun arises from the real motion
of the earth in its orbit, which is at the rate of about one
G 2

124? TO KNOW THE CONSTELLATIONS. Part II.

degree in a day, (see Def. 61. note, page 14.) whereas the
motion of the moon is about thirteen degrees in a day
(see the note, page 83.) The planets also, if observed on
successive nights, will appear to change their places
amongst the fixed stars, though when viewed from the
earth they will not always appear to move towards the
east, but sometimes towards the west, and at other times,
for several nights together they will appear stationary.

The apparent motion towards the west, and the station-
ary appearance, are merely optical and illusory, arising
from the combination of the earth's motion with that of
the planet. Viewed from the sun, the motion of the
planets is always in the same direction, and they never
appear to be stationary.

The apparent motion of the sun, and the real motion of
the moon and the planets from west to east, must be com-
bined with the diurnal motion of the earth on its axis
from west to east, or with the apparent motion of the
heavens from east to west. The apparent motion of the
stars from east to west is so rapid, when compared with the
real motion of the planets from west to east, that the latter
motion passes unnoticed by inattentive spectators.

CHAPTER II.

Of the Situation of the principal Constellations, and the
Manner of distinguishing them from each other.

THE stars, with respect to their apparent splendour,
are divided into different classes, called magnitudes. The
brightest are called stars of the first magnitude ; the next
to these in splendour, stars of the second magnitude,
and so on to those which are just perceptible to the
naked eye, and which are called stars of the sixth magni-
tude. Those which cannot be discerned without the as-
sistance of a telescope, are called Telescopic Stars, and are

Chap. II. TO KNOW THE CONSTELLATIONS.' 125

divided into classes of the seventh, eighth, &c. magni-
tudes.

The ancients divided the stars into different groups
called constellations (see Def. 91.), and gave particular
names to each, which names the greater part of them
have hitherto retained. The Pleiades and Orion are
mentioned in the sacred writings by Job, and Homer and
Hesiod describe several constellations by names which
are now in general use.

A knowledge of the principal constellations in the hea-
vens will be an useful acquisition to the student, and this
may be obtained by noting the time when they come to
the meridian, that is, to the south.

There are few persons who are unacquainted with the
seven (six) stars called the Pleiades, or the beautiful con-
stellation of Orion. * The Pleiades come to the meridian
of London about an hour before Aldebaranf, and Orion
culminates an hour after that star ; and, since the diurnal
difference of time of a star's culminating is nearly equal
to the diurnal difference of the sun's right ascension, viz.
about four minutes ; a star will rise, come to the meridian,
and set, nearly four minutes earlier every day, or about
two hours in a month.

The time of culminating of each of the zodiacal con-
stellations is given in the following table, and likewise the
semi-diurnal arc ; by which the time of rising and setting
may be ascertained sufficiently accurately for practice. In
the succeeding description, the principal constellations
which culminate with the zodiacal constellations are
pointed out, and their relative positions with respect to
each other are shewn ; so that the time of their coming to
the meridian may be easily found for any given day in the
year.

* This constellation is delineated, agreeably to its appearance in the
heavens, in Plate V.

f The time of this star's culminating on the first day of every
month, is given in the following table.

126

the Zodiacal Constellations on the first Day of every
ndon — N. B. The time is reckoned from noon to noo

me of culmina
i-diurnal Arc

a> <^^

"8^

S§

TO KNOW THE CONSTELLATIONS. Part II.

K K W K K S3 K 33 ffi 33 ffi a3

^ ,_( r-l r-H CM r-l CN

M|C*

,_( r_l i— t G^ Ol r— i

lor-ocN

^H i-l M CM

i— 1 i— 1 CM i—l

f-l CN i-H

OQ C?1

r-l GO GO

CM CM

r-4 GO ^H

v* •« ^xj T -* J WW W J I— 1 9 J

rH r-H rH r-l ^H Ol CM

Chap. II. TO KNOW THE CONSTELLATIONS. 127

The constellations and principal stars (visible at London}
which culminate with the zodiacal constellations are the fol-
lowingr, counting from the horizon*

1. With Aries (Arietis). The neck of Cetus, Triangu-
lum, Almaac in A-ndromeda, the head of Perseus, and

the feet of Cassiopeia Menkar in Cetus, Musca, the

head of Medusa, the body of Perseus, and the tail of
Camelopardalus, culminate three-quarters of an hour after
Arietis.

2. With Taurus (Aldebarari). Part of Eridanus and
Camelopardalus. — Algenib in Perseus culminates an hour
and a quarter before Aldebaran, the Pleiades three-quar-
ters of an hour before it, Rigel in Orion, and Capella in
Auriga, about half an hour after it.

3. With Gemini (Castor). Canis Major, Monoceros,
Canis Minor, and the Lynx. — Sirius culminates three-
quarters of an hour before Castor, and Procyon about six
minutes after Castor.

4. With Cancer (Acubene). The head of Hydra, the
tail of the Lynx, and the head of the Great Bear ; none
of which are of sufficient importance to attract the stu-
dent's particular attention.

5. With Leo (Regulus). Part of Hydra, Leo Minor,
and the shoulder of the Bear. The pointers in the Great
Bear come to the meridan (above the pole) an hour after
Regulus.

6. With Virgo (Spica). The middle star in the tail of
the Great Bear. — Coma Berenices, and Cor Caroli culmi-
nate an hour before Spica ; and Arcturus in Bootes about
an hour after Spica.

7. With Libra (« on the ecliptic). The left leg and
the head of Bootes. — The head of the serpent, and Corona
Borealis culminate three-quarters of an hour after » in
Libra.

8. With Scorpio (Antares). The left arm of Serpen-
tarius, and the club and body of Hercules.

9. With Sagittarius (the star in the bow marked S). Scu-
tum Sobieski, Cerberus in the left hand of Hercules, the
head and body of Draco, and the pole of the ecliptic. —

128 TO KNOW THE CONSTELLATIONS. Part II.

Vega in Lyra culminates a quarter of an hour after 8 in
Sagittarius.

10. With Capricornus (the star in the left horn marked
|8). The bow of Antinous, Vulpecula et Anser, and the
neck and body of Cygnus. — Altair in the Eagle comes to
the meridian half an hour before j5 Capricornus, and the
head of the Dolphin a quarter of an hour after it.

11. With Aquarius (the star in the right shoulder
marked a). The feet of Pegasus, the Lizard, and the
head of Cepheus. — Fomalhaut, in the Southern Fish,
culminates three quarters of an hour after a Aquarius,
and Markab, and Scheat in Pegasus an hour after it

12. With Pisces (the star in the string marked a). The
head of Aries, Triangulum, Almaac in Andromeda, the
sword of Perseus, and the feet of Cassiopeia. — a in the
head of Andromeda culminates nearly two hours before
« in Pisces, and Mirac, in Andromeda, about an hour
before it.

If the student observe the heavens in the month of Ja-
nuary, about ten o'clock in the evening, when the stars
are shining very bright, he will perceive towards the
south the Pleiades ; to the left hand of which, and a little
lower, are Aldebaran, of a reddish colour, and the Hyades
in the Bull as delineated below.

*
*

* *

TAURUS $

Farther to the left hand, and a little higher than the
Pleiades, is the remarkable constellation Auriga, which
has exactly the appearance of the figure annexed.

II. TO KNOW THE CONSTELLATIONS. 129

The highest star towards the right hand is Capella, the
lower star marked /3 is situated in the Bull's north horn,
and is near the right heel of Auriga.

Imagine a line to be drawn from Capella through the star
marked /3 towards the horizon, and it will pass through
the middle of the constellation Orion. This constellation
is delineated in Plate V., and is so brilliant and conspi-
cuous in the heavens that its figure when compared with
the plate will easily be known.

The three stars in a row form the Belt, and the large star
above the Belt towards the left-hand is Betelgeux, a star of
the first magnitude in Orion's right shoulder. About 26°
from Betelgeux, towards the left-hand, is Procyon, a star be-
tween the first and second magnitudes, in the constellation
Canis Minor. Between Betelgeux and Procyon, nearer to
the horizon, is Sirius, easily distinguished by its scintillation
and lustre ; these three stars form an equilateral triangle.

To the left hand of Auriga, and at about the same dis
tance from Capella as Aldebaran is, you will perceive Cas-
tor, a star of the first magnitude in Gemini; and near it
towards the left-hand is Pollux. There are four stars in
a line, about the half-way between Betelgeux and Castor ;
these»are the four feet of Gemini. Castor culminates on
the 1st of February, at half-past ten o'clock. Sirius cul-
minates three-quarters of an hour before Castor, and
Procyon six minutes after.

G 5

130 TO KNOW THE CONSTELLATIONS. Partll.

To the right hand of Auriga, and above the Pleiades,
in a line with Castor and Capella, is Algenib, a bright
star in the breast of Perseus, and farther to the right is
Almaac in Andromeda ; these two stars, with Algol in the
head of Medusa, form a triangle, of which Algol is the
nearest to the Pleiades. Imagine a line to be drawn from
the Pleiades, through Algol, and it will pass through Cas-
siopeia. This constellation is usually described by the
figure of an inverted chair ; but there are five bright stars
in it, which resemble the capital letter W, indifferently
made, much more than a chair.

To the right-hand of the Pleiades, at a considerable dis-
tance, viz. about 22°, is a Arietis, a star not very brilliant ;
a line drawn from the Pleiades through this star will pass
through Markab in Pegasus. The constellation Pegasus
is very remarkable : the three principal stars in it, with the
head of Andromeda, form a large square, of which
the four corner stars are all of the second magnitude.
The highest star towards the right-hand is Scheat ; it may
be easily known by a kind of isosceles triangle, formed
by three small stars, towards the right-hand of it ; one of
these stars is a little above Scheat.

** * .*>

r\r

Scheat

PEGASUS

Jlgenib

Chap. II. TO KNOW THE CONSTELLATIONS.

131

«**

If the student stand
facing the north, he
will perceive Ursa Ma-
jor, or the Great Bear,
the most conspicuous
constellation in the
heavens. It is visible
every fine starlight
night. The annexed
figure represents the
Great Bear when be-
low the pole. Of the
seven brilliant stars in
the Great Bear, those
marked a and £ are
called the two pointers,
because they direct the
eye to a bright star at
P, situated about a de-
gree and 31 minutes*
from the pole of the world, which star, from its vicinity to
that imaginary point, is named the polar star.

Ursa Minor, or the Little Bear, has nearly the same
shape as the Great Bear, but the situation is inverted,
and the seven stars are not so bright as those in the
Great Bear. An imaginary line drawn through the centre
of the square of the Great Bear, perpendicular to a line
supposed to join the stars a and &, will point out the
bright star marked (3 in the square of the Little Bear.
These constellations will assist the student in acquiring a
knowledge of the situation of others.

* In the Royal Astronomical Society's Catalogue (page ccxx.) the
difference of Right Ascension and Declination, together with the
Annual Precession of the Pole Star, is given for the first of January
of every ten years, as follows, from 1830 to 1860.

Year.

Right Ascens.
January 1.

Annual
Preces.

Declination.
January 1.

Annual
Preces.

1830
1840
1850
1860

h. m. sec.
0 59 30-76
1 2 10-32
1 5 0-29
1 8 1-73

Seconds.
+ 15-478
16-470
17-567
+ 18-784

88° 24' 8"'82
88 27 22-43
88 30 35-40
88 33 47-64

Seconds.
+ 19-371
19-309
19-240
+ 19163

132 TO KNOW THE CONSTELLATIONS. Part II.

For instance, the tail of Draco lies between the polar
star and the square of the Great Bear, and the figure ex-
tends in a serpentine direction towards the left-hand to a
considerable distance, where it is terminated by four bright
stars (in the head) forming nearly a square. An imaginary
line drawn through 5 and 7 in Ursa Major, southward, will
pass through the brightest star in Leo Minor, and through
Regulus in Leo Major. Regulus is easily distinguished,
being the southernmost of four bright stars.

By the foregoing description, with the assistance of a
celestial globe, it is presumed the learner may acquire a
knowledge of the principal constellations which appear in
the heavens in the winter. Those which present them-
selves in the summer are less conspicuous, but many of
them may be distinguished by the following description : —

If the student observe the heavens about ten o'clock in
the evening, at the beginning of May, he will see the
Great Bear near the zenith, above the pole. To the
right-hand of the pointers in the Great Bear, and near the
horizon, are Castor and Pollux, already described, and
farther to the right-hand is Auriga. An imaginary line
drawn through 8 and 7, as noticed before, will pass
through Leo Minor and through Regulus, and being con-
tinued in the same direction will pass through the heart of
Hydra. To the right-hand of Cor Hydrae, near the hori-
zon, a little more distant than Regulus, is Procyon in
Canis Minor, and at about the same distance, on the left-
hand, is Crater the Cup ; beyond which, in the same direc-
tion, is Corvus the Crow, being a kind of square formed
by four principal stars. An imaginary line drawn through
a and 7 in the Great Bear, as a diagonal to the square, will
pass through Cor Caroli near Coma Berenices, and through
fcpica Virginis. Spica Virginis, Arcturus in Bootes, and
Deneb in the Lion's tail, form an equilateral triangle, in
which Arcturus is the most elevated, and Deneb is situ-
ated towards the right-hand. A line connecting the first
and third stars in the tail of the Great Bear will pass
through Corona Borealis. This constellation is of an
oval form, and is composed of eight stars, three of which
are very bright, and appear close to each other. An
imaginary line drawn from Arcturus through Corona

THE MOTION OF THE FIXED STARS. 133

Borealis, will pass through the body of Hercules, beyond
which, in the same direction, is the bright star Vega in
Lyra. Below Corona Borealis is Serpens. When these
two constellations are on the meridian, Arcturus will be
on the right-hand and Vega on the left. Vega in Lyra.
Altair in the Eagle, and the head of the Dolphin, form an
isosceles triangle, of which Vega is at the vertex. Altair
is easily known, being the middlemost of the three bright
stars situated near to each other in a straight line. The
Dolphin lies to the left-hand of the Eagle, and is com-
posed of about five stars, four of which appear close to-
gether. Above the Dolphin, and to the left hand of Vega,
is Cygnus, a remarkable constellation in the milky way,
in the form of a large cross, below which is Pegasus already
described.

On the convex surface of the celestial globe the figures
of the constellations are reversed ; those which appear to
the right-hand on the globe are to the left-hand in the
heavens. The preceding account of their situations refers
to the heavens.

CHAPTER III.

Of the Motion of the Fixed Stars by the Precession of the
Equinoxes, by Aberration, and by the Nutation of the
Earth's Axis ; their proper Motions, Distance, variable
Appearance, fyc.

IT has already been shown (Def. 64.) that the intersec-
tion of the ecliptic with the equinoctial has a retrograde
motion of about 50£ seconds in a year, and that a revolu-
tion of the equinoctial points will be completed in about
25,791 years. Now, since the equinoctial changes its po-
sition with respect to the ecliptic, its axis will also be
changeable, and its poles, in the course of 25,791 years,
will describe a circular path in the heavens. Hence the
longitude, right ascension, and declination of every star
will be variable, and consequently the pole of the equi-
noctial cannot always be directed to the same star. The
star which at present is nearest to the north-pole of the
equinoctial is Alruccabah, a star of the second magnitude
in the tail of the Little Bear ; it is about a degree and

134- THE MOTION OF THE FIXED STARS. Part II.

and 31 min. from the pole. The nearest approach of
this star to the pole will be when its longitude is 90° ; it
will then be within a half a degree of the pole, and this will
happen in the year 2103 *, its longitude in the year 1800
being 85° 46' 10". Since the fixed stars complete a revolu-
tion about the axis of theecliptic in 25,791 years, any given
star will perform half a revolution in 12,895^ years ; there-
fore, in 12,895 years after 2103, that is, in the year 14,998,
the present polar star will be at its greatest distance from
the pole of the equinoctial, which will be upwards of forty-
five degrees, t In the year of the world 1704, the star
marked a in Draco was the polar-star, being at that time
within one sixth of a degree of the pole of the equinoctial.
This star lies half way between the middle star in the tail
of the Great Bear and y in the square of the Little Bear.

The aberration of the fixed stars is occasioned by the
velocity of light combined with that of the earth in its
orbit (see Def. 1 22.), by which each star apparently describes
an ellipsis about its mean place in a year ; the longer axis of
this ellipsis is about 40". The Nutation arises from the
attraction of the moon upon the equatorial parts of the
earth, by which the pole of the equinoctial describes an
ellipsis about its mean place as a centre. This ellipsis is
completed in a revolution of the moon's nodes, that is, in
18 years and 228 days ; the greater axis being in the sol-
stitial colure and equal to 19"'l, and the kss axis in the
equinoctial colure and equal to 14"-2. J

Dr. Maskelym observes that many, if not all the fixed
stars, have small motions among themselves, which are
called their proper motions ; the cause and laws of which
are hid, for the present, in almost equal obscurity. By
comparing his observations with others, he found the an-
nual proper motion of the following stars, in right ascen-
sion, to be, of Sirius, — 0"-63 ; of Castor, --0"-28 ; of
Procyon,— 0"'88; of Pollux,— 0"-93; ofRegulus,—Q"-4>l;

* 50V : 1 year :: 90<>— 85° 46' 10" : 303 years, which, added
to 1800, gives 2 1 03.

t Sir J. Herschel states that after a lapse of about 12,000 years,
the star a Lyrae will be the pole star, and will be within about 5° of
the north pole.

\ Dr. Mackay on the Longitude, vol. i. third edition, page 11.

Chap. HI. THE MOTION OF THE FIXED STARS. 135

ofArcturus, — I" A; of a. Aquilce + 0".57; and Sirius in-
creased in north polar distance + 1".20; Arcturus, + 2".01.

The magnitudes of the fixed stars will probably for ever
remain unknown ; all that we can have any reason to ex-
pect, is a mere approximation founded on conjecture. —
From a comparison of the light afforded by a fixed star,
and that of the sun, it has been concluded that the mag-
nitudes of the stars do not differ materially from that of
the sun. The different apparent magnitudes of the stars
is supposed to arise from their different distances; for the
young astronomer must not imagine that all the fixed stars
are placed in a concave hemisphere, as they appear in the
heavens, or on a convex surface, as they are represented
on a celestial globe.

From a series of accurate observations by Dr. Bradley
on y Draconis, he inferred that its annual parallax did
not amount to a single second ; that is, the diameter of
the earth's annual orbit, which is not less than 190 mil-
lions of miles, would not form an angle at this star of one
second in magnitude ; or that it appeared in the same
point of the heavens during the earth's annual course
round the sun.

The same author calculates the distance of y Draconis
from the earth to be 400,000 times that of the sun, or
38,000,000,000,000 miles, and the distance of the nearest
fixed star from the earth to be 40,000 times the diameter
of the earth's orbit, or 7,600,000,000,000 miles. These
distances are so immensely great, that it is impossible for
the fixed stars to shine by the light of the sun reflected
from their surfaces : they must therefore be of the same
nature with the sun, and like him shine by their own
light.

The number of the fixed stars is almost infinite, though
the number which may be seen by the naked eye in the
whole heavens does not exceed, and perhaps falls short of
8000*, comprehending all the stars from the first to the
sixth magnitude inclusive ; but a good telescope, directed

* By adding up the numbers of stars in the first column, as taken
from the Royal Astronomical Society's Catalogue, given at pages 27,
28, and 29, the sum will be found to be 2930. See page 26.

136 THE MOTION OF THE FIXED STARS. Part II.

almost indifferently to any point in the heavens, discovers
multitudes of stars invisible to the naked eye. That bright
irregular zone, the milky way, has been very carefully ex-
amined by Dr. Herschel ; who, in the space of a quarter
of an hour, saw 116,000* stars pass through the field of
view of a telescope of only 15' aperture.

The fixed stars are the only marks by which astrono-
mers are enabled to judge of the course of the moveable
ones, because they do not vary their relative situations.
Thus, in contemplating any number of fixed stars, which
to our view form a triangle, a four-sided figure, or any
other, we shall find that they always retain the same re-
lative situation, and that they have had the same situation
for some thousands of years, viz. from the earliest records
of authentic history. But as there are few general rules
with(*ut some exceptions, so this general inference is like-
wise subject to restrictions. Several stars, whose situa-
tions were formerly marked with precision, are no longer
to be found ; new ones have also been discovered, which
were unknown to the ancients ; while numbers seem gra-
dually to vanish, and others appear to have a periodical
increase and decrease of magnitude, f Dr. Herschel, in
the Philosophical Transactions for 1783, has given a large

* Dr. Herschel says, " in the most crowded part of the milky way
" I have had fields of view that contained no less than 588 stars, and
" these were continued for many minutes, so that in one quarter of
" an hour's time there passed no less than 1 1 6,000 stars through the
" field of view of my telescope. — The breadth of my sweep was
" 2° 26', to which must be added 15' for the two semi-diameters of
"the field. Then putting 161' = a, the number of fields in 15' of
" time; -7854 = 6, the proportion of a circle to 1, its circumscribed
" square ; $ = sine of 74° 22' the polar distance from the middle of
" the sweep reduced to the present time ; and 588 = «, the number of

" stars in a field of view, we have a<^$ =116076 stars.

This calculation is founded on a supposition that the stars were
equally disseminated through the whole field of view of the telescope.

J In 1803, after an inquiry of 25 years, Sir William Herschel an-
nounced to the world, through the medium of the Transactions of the
Royal Society, that there exist sidereal systems composed of two stars,
revolving about each other in regular orbits, and constituting what
may be termed binary stars.

Chap. III. THE MOTION OF THE FIXED STARS. 137

collection of stars which were formerly seen, but are now
lost, together with a catalogue of variable stars, and of
new stars.

The periodical variation of Algol or /3 Persei, is about
62 hours ; its greatest brightness is of the second magni-
tude, and least of the fifth. It varies from the second
magnitude to the fifth in about 3-J hours, and back again
in the same time, retaining its greatest brightness for the
remainder of its period.

The fixed stars do not appear to be all regularly dis-
seminated through the heavens, some of them appearing
in clusters ; and require a large magnifying power to dis-
tinguish separately the stars which compose them. With
a small magnifying power, they only appear as minute
whitish spots, like small light clouds, and thence are called
nebula. Sir John Herschel has given a catalogue of 2500
nebula and clusters of stars, with which the starry heavens
appear to be replete. The largest nebula is the milky
way, already noticed at page 36.

From an attentive examination of the stars with good
telescopes, many which appear single to the naked eye
have been found to consist of two, three, or more stars.
Dr. Herschel, by the help of his improved telescopes,
has discovered nearly 700 such stars. Thus a. Herculis,
5 Lyra, a Geminorum, y Andromeda, (A Her cults, and many
others, are double stars; v Lyra, is a triple star; and
£ Lyra, /3 Lyra, X Orionis, and f Libra, are quadruple
stars.*

* Since the publication of the last edition of this work, M. Bessel
has made one of the greatest discoveries of modern times, by having
ascertained the parallax of the double star a Signi. He found by
various observations made from August, 1837, to March, 1840, that its
parallax did not exceed 0" '31 ; hence its distance from our earth is
nearly 670,000 times that of the sun, or 63,650,000,000,000 miles.
This immense distance can better be conceived, when we state that if
a cannon ball were to traverse this vast space, at the rate of 20 miles
a minute, it would occupy more than six millions of years in coming
from that star to our earth ; and if a body could be projected from our
earth to that star, at the rate of 30 miles an hour, which is about the
rate the carriages on railroads travel, it would occupy at least ninety-
six millions of years.

138

THE ASTRONOMICAL QUADRANT. Part II.

CHAPTER IV.

The Method of measuring the Altitudes, Zenith Distances,
fyc. of the heavenly Bodies, including a Description of
the Astronomical Quadrant, Circular Instrument, and
Transit Instrument.

IT is of importance to the young astronomer to know
in what manner the altitudes of the heavenly bodies are
determined ; for which reason the most simple instru-
ments for that purpose are here described. This descrip-
tion, however, must be considered as contracted and im-
perfect, since the various adjustments of the instruments,
and the manner of using them to advantage, can be ac-
quired only by practice.

The astronomi-
cal quadrant is ge-
nerally made of
brass; the arc HB
is divided into 90
equal parts, called
degrees, and each
degree is subdi-
vided into smaller
parts, according to
the size of the
instrument. Tt is
a telescope move-
able about a cen-
tre, c. From the
centre c is sus-
pended a weight
p hanging freely
in the direction of
gravity, or perpen-
dicularly to the earth's surface, the line CP is called a
plumb-line.

Now, if the plane of the instrument, by proper adjust-
ments, be made to coincide with the plane of the meridian

Chap. IV. THE ASTRONOMICAL QUADRANT. 139

of any place, and the plumb-line CP at the same time
be made to hang exactly over the division marked 90-; it
is obvious, that if the telescope T t be directed towards
any star s in the plane of the meridian, the number of
degrees between H and T on the arc, will mark the star's
altitude os on the meridian, and the number of the de-
grees between T and B will mark its zenith distance sz :
for the imaginary quadrant oz of the meridian is supposed
to be similarly divided to the instrumental quadrant HB,
and to contain 90 degrees between the horizon and the
zenith. If the star be in the horizon at o, the telescope
will coincide with HO or be parallel to it ; if the star be in
the zenith at z, the telescope will coincide with the plumb-
line CP. In the figure annexed the telescope is directed
towards a star having about 40 degrees of altitude. The
quadrant may be placed in the plane of any other vertical
circle as well as in that which passes through the meridian,
and then it will measure altitudes in that vertical circle.

When the quadrant is fixed against a vertical wall in
the plane of the meridian, it is called a mural quadrant. —
Such are the quadrants in the Royal Observatory at
Greenwich.

The astronomical instrument now generally used is
an improvement upon the quadrant here described ; and
this improvement consists, chiefly, in putting together four
quadrants, and thereby forming a circular instrument.

The figure in Plate VI. is a representation of a small
model of the large circles used in observatories.* The
vertical circle AB is formed by four quadrants, and the
telescope CD is not moveable on the arc of the instrument
as before, but is attached to the circle, and moves only
when the circle itself moves. When the telescope is
placed horizontal, viz. in the direction AB, the divisions
marked o will be at z and M. If the telescope be directed
to any star, the arc of the circle from the telescope at c

* Tliis figure is copied from a neiv, portable, and useful instrument^
made by Messrs. W. and S. Jones, of Holborn, who very kindly furl
nished the Author with a drawing of it, from which drawing the plate
is engraven.

14-0 THE ASTRONOMICAL QUADRANT. Part II.

to M will shew the zenith distance of the star, and the arc
from M to the division marked o will shew its altitude ; if
the instrument be situated in the plane of the meridian, it
will shew the altitude and polar distance of any sfcar, or
the star's declination ; for having the latitude of a place
given, and the meridian altitude of a star, the declination
of that star is readily determined.

The vertical circle of the instrument here described is
graduated as in the figure ; at M is a Nonius scale, with a
microscope, which reads off to one minute of a degree ;
the slow motion of the circle, for accuracy of observation,
is produced by turning the screw at G.

The achromatic telescope CD is contrived by a reflect-
ing eye-piece to admit of observations conveniently to the
zenith. The axis of the vertical circle reverses for due
adjustment, and is made level by the small suspended
spirit-level L. The wires of the telescope are illuminated
at night by a small reflector placed in the inside of the axis,
and the light is transmitted through the axis by means of
a small lighted lamp occasionally attached to it.

The base of the instrument, which supports the vertical
circle, has an horizontal motion, the slow motion of which
is produced by turning the screw at o. By the motion
of the horizontal circle the azimuths of the celestial ob-
jects are obtained, and this circle is placed truly hori-
zontal by means of the two spirit-levels s, s ; the screws
at E, E, E, are for the purpose of fixing the base in its
proper position.

When the vertical circle is truly placed in the plane of
the meridian, the vertical wires of the telescope will an-
swer the purpose of a transit instrument.

By the assistance of this instrument the altitude of the
sun's centre may be observed from day to day, and this
altitude wiH be found to vary continually by unequal dif-
ferences : also the successive transits of the fixed stars
over the meridian may be ascertained.

The principal fixed instrument used in all the great observatories
is the Mural Circle, which, as its name imports, is usually fixed to a
wall, and in the meridian, for the purpose of measuring the distance
of stars from the pole or the zenith.

Chap. V. OF THE SOLAR SYSTEM. 141

CHAPTER V.

Of the Solar System. (Plate II. Fig. 1.)

THE solar system is so called because the sun is sup-
posed to be situated in a certain point termed the centre
of the system, having all the planets revolving round him
at different distances, . and in different periods of time.
This is likewise called the Copernican system.

I. OF THE SUN.

The sun is situated near the centre of the orbits of all
the planets, and has a rotation about his axis, the period of
which is determined from the motion of spots which pass
from east to west across bis disc. By carefully observing
the time which intervenes between a spot's disappearing
on the western limb of the sun and its next subsequent
disappearance, the period of its apparent revolution will be
obtained, which is found to be twenty-seven days, seven
hours, and thirty-seven minutes. As the earth, however,
revolves round the sun in the same direction, it is evident
that this spot must have performed something more than
a complete revolution, and consequently that the true
period of the sun's rotation on its axis is something less
than the time indicated by the apparent motion of the
spot, and may be found by the following proportion, viz.
as the time in which the earth completes one revolution in
its orbit, added to the apparent time of the revolution of
the spot, is to the time in which the earth completes one
revolution only, so is the apparent time of the revolution
of the spot to the true time of the sun's rotation on its
axis, which is accordingly found to be twenty-five days,
nine hours, and fifty-nine minutes, + some odd seconds.*

* 365 days 5 hours 48 min. + 27 days 7 hours 37 min.=392 days
13 hours 25 min. : 365 days 5 hours 48 min. : : 27 days 7 hours 37
min. : 25 days 9 hours 59 min. + The above proportion will be found
sufficiently exact for general purposes, but is not strictly accurate, the
arc being measured on the ecliptic instead of the sun's equator ; there-
is also some inaccuracy arising from the earth's real motion not being
performed equally in a true circle : the error is, however, too trifling to

142 OF THE SOLAR SYSTEM. Part II.

The sun is likewise agitated by a small motion round
the centre of gravity of the solar system, occasioned by
the various attractions of the surrounding planets ; but,
as this centre of gravity is generally within the body of
the sun *, astronomers generally consider the sun as the
centre of the system, round which all the planets revolve.
As the sun revolves on an axis, his figure is not strictly
that of a globe, but a little flatted at the poles ; and
his axis makes an angle of seven and a half degrees f with
a perpendicular to the plane of the earth's orbit. As
the sun's apparent diameter is greater in December than
in June, it follows that the sun is nearer to the earth
in our winter than it is in summer ; for the apparent mag-
nitude of a distant body diminishes as the distance in-
creases. The mean apparent diameter of the sun is stated
to be 32' 2" ; hence, taking the distance of the sun from
the earth to be 95 millions of miles, as before determined J,
its real diameter will be 886149 miles; or above one
hundred and eleven times that of the earth.

II. OF MERCURY. $

Mercury is the least of all the planets, whose magnitudes
are accurately known, and the nearest to the sun. The
inclination of its axis to the plane of its orbit is unknown.

require further notice. M. Cassini determined the time of the sun's
rotation to be 25 days 14 hours 4 min., and Delambre's calculations
make it 25 '01 154 days. — ED.

* Sir I. Newton's Princip. Book iii. Prop. 11. and 12.

f See Baily's Astronomical Tables and Formulae, p. 5.

\ The semi-diameter of the earth has been determined at page 63.
in the note, to be 3982 miles ; and the distance of the earth from the
sun is 2388*284 semi-diameters of the earth. See the note, page 63.
Now the apparent semi-diameter mn of the sun (Plate IV. Fig. 3.)
is measured by the angle mon = 32' 2" ; hence the angle omn = the

angle onm = 18°°~32/ 2//=89° 43' 59"; and on account of the

distance of the sun from the earth, om, oc, and on may be considered

as equal. Hence,

Sine omn 89° 43' 59'' 9*9999953

Is to 23882-84 semi-diameters 4*3780860

As sine mon 32' 2" 7*9693152

Is to 222*5388 semi-diameters 2*3474059

Now, 222*5388 x 3982 = 886149*5016 miles, the diameter of

the sun, the cube of which divided by the cube of 7964, the diameter

Chap. V. OF THE SOLAR SYSTEM. 143

The rotation on his axis is accomplished in 24 hrs. 5 m.
28'3 s. * Mercury is seen through a telescope sometimes
in the form of a half moon, and sometimes a little more
or less than half its disc is seen ; hence it is inferred, that
it has the same phases as the moon, except that it
never appears quite' round, because its enlightened side
is never turned directly towards us, unless when it is
so near the sun as to become invisible, by reason of the
splendour of the sun's rays. — The enlightened side of
this planet being always towards the sun, and it never
appearing round, are evident proofs that it shines not
by its own light. The best observations of this planet are
those made when it is seen on the sun's disc, called its
transit ; for, in its lower conjunction, it sometimes passes
before the sun, like a little spot There was a transit of
Mercury on the 4th of November, 1822, which was not
visible at Greenwich.-}- That node from which Mercury as-
cends northward above the ecliptic is in the fifteenth degree
of Taurus J; and consequently the opposite or descending
node is in the fifteenth degree of Scorpio. The sun is
in the fifteenth degree of Taurus on the 6th of May,
and in the fifteenth of Scorpio on the 7th of Novem-
ber; and when Mercury comes to either of his nodes

of the earth, gives 1377613 times the sun is larger than the earth.
Its mass is only 354936 times greater, and its density is -^f^ or '2543,
which is about one quarter that of the eatth.

* By observations on the daily change of appearance in Mercury's
horns, its diurnal rotation was found by Schroeter to be performed in
24 hours 5 minutes and 28'3 seconds. He also detected spots, and
even mountains, in Mercury, and succeeded in measuring the altitude
of two of them, one of which he found to be ten miles and three
quarters in height, being almost three times as high as Chimbora9O.

t The last transit of Mercury was on the 5th of May, 1 832, when,
had the weather proved favourable, Mercury would have been visible
as a black spot on the Sun's disc for nearly seven hours. " The five
next transits which will be visible in this country will occur at the
following dates, May 8th, 1845 ; Nov. 9th, 1848 ; Nov. llth, 1861 ;
Nov. 4th, 1868 ; May 6th, 1878."— F. Saily, p. 12.

J The place of Mercury's ascending node at the commencement
of 1801 was 45° 57' 30"'9 ; having a motion to the westward, every
year, of 7". 82. But, when referred to the ecliptic, the place of
the node will (on account of the precession of the equinoxes) fall more
to the eastward by 42" -3 m. a year, or 1° 10' 30" in a century.

1 44 OF THE SOLAR SYSTEM. Part II.

at its inferior conjunction (viz. when it is between
the earth and the sun), it will pass over the sun's
disc, if it happen on or near the days above mentioned ;
but in all other parts of its orbit, it goes either above
or below the sun, and consequently its conjunctions are
invisible.

Mercury performs its periodical revolution round the
sun in 87 d. 23 h. 15 min. 43*9 sec. ; its greatest elong-
ation is 28° 20', distance from the sun 36814721 * miles ;

* According to Laplace, Mercury's siderial period is 87.969258
days, and his mean distance from the sun is. 387098, assuming the
earth's distance as a standard and equal to 1 .

The distance of Mercury, or any planet, from the sun, may be
found by Kepler s rule. Thus the square of the time which the
earth takes to revolve round the sun, is to the cube of the mean
distance of the earth from the sun, as the square of the time
which any other planet takes to revolve round the sun, is to
the cube of its mean distance ; the cube root of which will give
the distance sought. Or, which is shorter, divide the square of tht
time in which any planet revolves round the sun, by the square
of the time in which the earth revolves round the sun, the cube
root of the quotient will give the relative distance of the planet from
the sun. This relative distance, multiplied by the mean distance of
the earth from the sun, will give the mean distance of the planet from
the sun.

First for Mercury. The earth revolves round the sun in 365d. 5h. 48
min. 48 sec = 31556928 sec. the square of which is 995839704797184,
a constant divisor for all the planets, and 23882.84, the distance
of the earth from the sun in semi -diameters (see page 68, note)
will be a constant multiplier. 87 d. 23 h. 15m. 43 sec. = 7600543
sec. the square of which is 57768253894849. This square di-
vided by the former, gives .0580096 nearly, the cube-root of
which is .38710991, the distance of Mercury from the sun, sup-
posing the distance of the earth from the sun to be an unit. .38710991
x 23882.84 = 9245.2841 distance of Mercury from the sun in
semi-diameters of the earth; hence 9245.2841 x 3982, radius of
the earth, = 36814721 miles, the mean distance of Mercury from the
sun.

The distance of the inferior planets from the sun may be found by
their elongations. M. de la Lande has calculated that, when Mer-
cury is in his aphelion, and the earth in its perigee, the greatest elong-
ation of Mercury is 28° 20' ; but when Mercury is in his perihelion,
and the earth in its apogee, the greatest elongation is 17° 36'; the
medium, therefore, is 22° 58'. Hence, in the triangle, SEV. (Plate II.

Chap. V. OF THE SOLAR SYSTEM. 145

the eccentricity of its orbit is estimated at one -fifth of
its mean distance from the sun ; its apparent diameter
11"; hence its real diameter is 3108 miles*; and its
magnitude about one-sixteenth of the magnitude of the
earth.

Mercury emits a bright white light ; it appears a
little after sun-set, and again a little before sun-rise ;
but, on account of its nearness to the sun, and the
smallness of its magnitude, it is seldom seen. The
light and heat which this planet receives from the sun,
are about seven times greater than the light and heat

Fig. 2.) the angle SEV = 22° 58', the distance of the earth from the
sun SE = 23882.84 semi-diameters, and EVS is a right angle.

Radius, sine of 90° 10.0000000

Is to SE = 23882.84 4.3780860

As sine of 22° 58' 9.5912823

Is to 9318.976 semi-diameters 3.9693683

Hence 9318976 x 3982 = 37108162 miles, the distance of Mercury
from the sun by this method : but an error of a few seconds in the
elongation will make a considerable difference.

* The mean distance of the earth from the sun is 23882.84
semidiam., and Mercury's distance 9245.2841 semi-diam. : the
difference is 14637.5559 semi-diam. : the distance of Mercury from
the earth : and, as the magnitudes of all bodies vary inversely as
their distances, we have by the rule-of-three inverse 14637.5559 :
11": : 23882.84: 6 .74179", the apparent diameter of Mercury, at
a distance from the earth equal to that of the sun. Now the mean
apparent diameter of the sun is 32' 2", and its real diameter 886149
miles; hence 32' 2" : 886149 m. :: 6" -741 7 9 : 3108 miles the
diameter of Mercury : and, if the cube of the diameter of the earth
be divided by the cube of the diameter of mercury, the quotient
will be 16-8 times the magnitude of the earth exceeds that of
Mercury.

The diameter of Mercury might have been found exactly in the
same manner as the diameter of the sun was found in the the note
page 142. using 11" instead of 32' 2", and 14637 '5559 semi-diam.
instead of 23882-84 semi-diam. : the result of the operation in
this case will be -78061 semi-diam. of the earth; hence -78061
x 3982 = 3108 miles the diameter of Mercury exactly as above.
It has been remarked at page 68. that the apparent diameters
of the planets are measured by a micrometer, said to be invented
by M. Azout a Frenchman ; but it appears, from the Philo-
sophical Transactions, that it was invented by Mr. Gascoigne, an
Englishman.

14-6 OF THE SOLAR SYSTEM. Part II.

which the earth receives. * The orbit of Mercury makes
an angle of seven degrees with the ecliptic, and it
revolves round the sun at the rate of upwards of ^one
hundred and nine thousand miles per hour, f The
manner in which the earth revolves round the sun has
already been explained at page 66, and as all the other
planets move in a similar manner in elliptical orbits, hav-
ing the sun in one of the foci, what has been observed
respecting the earth will be equally applicable to all
the planets.

III. OF VENUS $ .

Venus is the brightest, and, to appearance, the largest
of all the planets ; her light is distinguished from that of
the other planets by its brilliancy and whiteness, which
are so considerable that, in a dusky place, she causes an
object to cast a sensible shadow. Venus, when viewed
through a telescope, appears to have all the phases of the
moon, from the crescent to the enlightened hemisphere;
though she is seldom seen perfectly round. Her illu-
minated part is constantly turned towards the sun ; hence,
the convex part of her crescent is turned towards the
east when she is a morning star, and towards the west
when she is an evening star ; for when Venus is west of

* As the effects of light and heat are reciprocally proportional to the
squares of the distances from the centre whence they are propagated, if
you divide the square of the earth's distance from the sun, by the square
of Mercury's distance from the sun, the quotient will shew the com-
parative heat of Mercury to that of the earth.

t This is found in the same manner as for the earth in page 68. Thus
if you double the distance of any planet from the sun, then multiply by
355, and divide the last product by 113, you obtain the circumference
of the planet's orbit in miles. This circumference, divided by the num-
ber of hours in the planet's year, will give the number of miles yer
hour which that planet travels round the sun : a general rule for all the
frtanets. Hence,

The circumference of Mercury's orbit will be found to be 23131S733
.717 miles ; then 87d. 23h. 15*' 43'' : 231313733.717 miles : : 1 h. ;
109561 miles Mercury travels per hour.

Chap. V. OF THE SOLAR SYSTEM. 147

the sun, as seen from the earth, that is, when her longi-
tude is less than the sun's longitude, she rises before
him in the morning, and is then called a morning star ;
but when she is east of the sun, viz. when her longitude
is greater than the sun's longitude, she shines in the even-
ing after the sun sets, and is then called an evening star.

Venus is a morning star, or appears west of the sun for
about 290 days, and she is an evening star, or appears
east of the sun, for nearly the same length of time, though
she performs her whole revolution round the sun in 224-
days 16 hours 49 minutes 10 seconds. A very natural
question here may be asked, viz. Why Venus appears a
longer time to the eastward or westward of the sun
than the whole time of her entire revolution round him ?
This is easily answered, by considering that, while Venus is
going round the sun, the earth is going round him the same
way, though slower than Venus, and therefore the relative
motion of Venus is slower than her absolute motion.

Sometimes Venus is seen on the disc of the sun in the
form of a dark round spot. These appearances happen but
seldom, viz. they can happen only when Venus is between
the earth and the sun, and when the earth is nearly in a
line with one of the nodes of Venus. * The last transit of
Venus was in 1769, and the two next transits, in succes-
sion, will fall on the 8th of December, 1874, and on the
6th of December, 1882. The time which this planet
takes to revolve on its axis is 23 hours 21 minutes 7'2 se-
conds.f The inclination of its axis to the plane of its
orbit has been given by different astronomers ; but Dr,
Herschel, from a long series of observations on this planet,
published in the Philosophical Transactions for 1793, con-
cludes that the position of its axis is uncertain ; that its
atmosphere is very considerable ; that it has probably

* The place of the ascending node of Venus at the commencement
of 1801 was 74° 54* 12'' '9, having a motion to the westward every year
of 17" '6. But when referred to the ecliptic, the place of the node
will (on account of the precession of the equinoxes) fall more to the
eastward by 32" -5 in a year. F. JSaily. Its variation in 100 years is
51' 58" -99. — Laplace.

f Schroeter states the time of her diurnal rotation ta be 23 hours
20 minutes 54 seconds.

H 2

14-8 OF THE SOLAR SYSTEM. Part II.

inequalities on its surface, yet he cannot discover any
mountains. The apparent diameter of Venus is stated
to be 58".79; the eccentricity of her orbit 473100
miles * ; her greatest elongation 47° 48' ; her revolution
round the sun is performed in 224 d. 16h. 49m. 10 sec. f
as before stated; and, if her apparent diameter be taken
as above, her true diameter will be 7498 miles J, and
her magnitude something less than that of the earth } ;
likewise her distance from the sun will be found to be
G8791752 miles.

The light and heat which this planet receives from
the sun are about double of what the earth receives. ||

* For, according to M. de la Lande, if the mean distance of the
«aith be 100000, the eccentricity of Venus will be 498 ; hence, when
the distance is 95 millions of miles, the eccentricity will be 473100
miles.

t The seconds in this time = 19414150, the square of which is
376909220222500, this divided by 99583970'4797 184 (see the note,
page 144.) gives .3784838, &c. the cube root of which is .7233511 ;
this, multiplied by 23882.84, produces 17275.678585 semi-diam.
which, multiplied by 3982 = 68791752 miles, the distance of Venus
from the sun.

According to Laplace, the sidereal revolution of Venus is 224.700824
days, and her mean distance from the sun is .723332.

M. de la Lande has found the greatest elongations of Venus to be
47° 48' and 44° 57' when in similar situations to Mercury, mentioned
in the note, page 145. ; the medium is 46° 22' 30", using this angle
and the very same calculation as in the note page 145., the distance of
Venus from the sun will be found =17288. 09 semi-diameters of the
earth; hence the distance will be had = 68841 174 miles, astonishingly
near to the distance found by Kepler's rule, considering the great
difference in the principles of calculation, and a strong proof of the
truth of the Copernican system.

$ Here, (as in the note, page 145.) 23882.84—17275.678585 =
6607.16145 semi-diam. distance of Venus from the earth; hence,
inversely, 6607.16145 : 58''.79 : I 23882.84 : 16''.26419, and 32' 2":
886149 : : 16". 2641 9 : 7498 miles, the diameter of Venus. Or, by
trigonometry, using the angle 58".79, and distance 6607.16145, the
result is 1.88314; x 3982 = 7498 miles.

§ Sir J. F. W. Herschel quotes 7800 miles for the diameter cf
Venus.

|| These are found by dividing the square of the earth's distance
from the sun by the square of the distance of Venus from the sun.

The earth's distance from the sun is 95000000 miles, the square of
which is 9025000000000000, the distance of Venus from the sun is
68791752 miles, the square of which is 4732305143229504 ; the for-
mer square divided by the latter gives 1.907 for the quotient.

Chap. V. OF THE SOLAR SYSTEM. 149

The orbit of Venus makes an angle of 3° 23'28".5with
the ecliptic, and she revolves round the sun at the rate
of upwards of eighty thousand miles per hour. * This
planet, like Mercury, never departs from the sun ; she
is only visible a few hours in the morning before the sun
rises, or in the evening after he sets ; an evident proof
that the orbits of these planets are contained within the
orbit of the earth, otherwise they would be seen in oppo-
sition to the sun, or above the horizon at midnight.

* IV. OF THE EARTH ©, and its SATELLITE THE MOON ]) .

The figure and the magnitude of the earth have
been already explained in Chapter III. Part I.; and its
diurnal and annual revolutions round the sun, distance
from the sun, seasons of the year, &c. have been shown in
Chapter IV. : as it would be superfluous to repeat those par-
ticulars here, this chapter is confined entirely to the moon.

The moon being the nearest celestial body to the eartli,
and, next to the sun, the most resplendent in appearance,
has excited the attention of astronomers in all ages. The
Hebrews, the Greeks, the Romans, and, in general, all
the ancients, used to assemble at the time of new or
full moon, to discharge the duties of piety and gratitude
for its manifold uses. The day being measured by
observing the time which the sun took in apparently
moving from any meridian to the same again, so the
month was measured by the number of days elapsed
from new moon to new moon ; this month was supposed
to be completed in thirty daysf ; and when the motion

* By the process mentioned in the note, page 1 46., the circumference
of the orbit of Venus will be found to be 432231362.123 miles ; then,
as 224 d. 16 h. 49m. lOsec. ; 432231362.123 miles :: Ih. : 80149
miles Venus travels per hour.

t The Rev. Mr. Costard, in his History of Astronomy, supposes
that the oldest measure of time (taken from the revolutions of the
heavenly bodies) was a month ; and, after the length of the year was
discovered, the ecliptic, and all other circles, were divided into 360
eiual parts, called degrees, because 30 d. x 12 = 360 days, the
length of the year. — Hist, of Astr. p. 44. In an account of the Pelew
Islands, we are told that the inhabitants reckoned their time by
months, and not by years ; for, when the king intrusted his son to the
care of Captain Wilson, he enquired how many moons would elapse
H 3

150 OF THE SOLAR SYSTEM. Part II.

of the moon came to be compared with, and adjusted to,
the apparent motion of the sun, twelve of these months
were thought to correspond exactly with the sun's annual
course. The lunar month is of two sorts, periodical and
synodical. A tropical month is the time in which the
moon finishes her course round the earth, and consists of
27 days 7 hours 43 minutes 5 seconds * ; and a synodical
month is the time elapsed from new moon to new moon,
and consists of 29 days 12 hours 44 minutes 2.8 seconds.
The synodical month was probably the only one observed
in the infancy of astronomy.-|-

The orbit of the moon is nearly elliptical, having the
earth in one of its foci ; but the eccentricity of this ellip-
sis is variable, being the greatest when the line of the ap-
sides is in the syzygies, for then the transverse axis of the
moon's orbit is lengthened ; and the least when the trans-
verse axis is in the quadratures, for then the conjugate
axis is lengthened, and consequently the orbit approaches
nearer to a circle. The moon in her revolution round the
earth would always describe the same ellipsis, were that
revolution undisturbed by the action of the sun ; the
principal axis of her orbit would remain at rest, and be
always of the same quantity; her periodic times would all
be equal, and the inclination of her orbit to the ecliptic
and the place of her nodes would be invariable ; but
her motions being disturbed by the action of the sun,
they become subject to so many irregularities, that to
calculate the moon's place truly, and to establish the ele-
ments of her theory, are almost insuperable difficulties.

before he might expect the return of his son. The inhabitants of
these islands were totally ignorant of the arts and sciences.

* Tropical revolution 27.321582 days, synodical 29.530588.
M. Laplace.

f The sidereal revolution of the moon is performed in 27.321661
days, or 27 d. 7 h. 43 m. 1 1.51 s., being the time she employs in
moving from any fixed star to the same fixed star again.

The anomalistic revolution is performed in 27.5546 days, or in 27 d.
13 h. 18 m. 37.44 s., being the time the moon takes to move from
perigee to perigee. The interval from node to node is called the
nodical period, and is shorter than any of the other periods, being
performed in 27.212217 days, or in 27 days, 5 h. 5 m. 35.6 seconds.

Chap. V. OF THE SOLAR SYSTEM. 151

The orbit of the moon is inclined to the ecliptic in an
angle, which is variable from 5° to 5° 18', consequently
it is inclined in an angle of 5° 9' at a medium. The motion
of the moon's nodes, or places .where her orbit crosses the
orbit of the earth, is westward, or contrary to the order
of the signs: this motion is likewise irregular, but by
comparing together a great number of distant observations,
fhe mean annual retrograde motion is found to be about
1 9D 19' 42*3" so that the nodes make a complete retrograde
revolution from any point of the ecliptic to the same again
in about 18 years 228 days 9 hours. The axis of the
moon is almost perpendicular to the plane of the ecliptic,
the angle being 88° 17', consequently she has little or no
diversity of seasons. The moon turns round her axis,
from the sun to the sun again, in 29 days 12 hours 44
minutes 3 seconds, which is exactly the time that she
takes to go round her orbit from new moon to new moon ;
she therefore has constantly the same side turned towards
the earth. This, however, is subject to a small variation,
called the libration * of the moon, so that she sometimes
turns a little more of the one side of her face towards the
earth, and sometimes a little more of the other, arising
from her uniform motion on her axis and unequal motion
in her orbit : this is called her libration in longitude.f —
The moon likewise appears to have a kind of vacillating
motion, which presents to our view sometimes more and
sometimes less of the spots on her surface towards each
pole ; this arises from the axis of the moon making an
angle of about 1° 43' with a perpendicular to the plane of
the ecliptic; and as this axis maintains its parallelism
during the moon's revolution round the earth, it must
necessarily change its situation to an observer on the earth ;
this is called the moon's libration in latitude. J

* A lunar globe was published a few years ago by Mr. Itussel,
which shews not only the libration of the moon in the most perfect
manner, but is a complete picture of the mountains, pits, and shades,
on her surface.

•f* The libration, in longitude, at its maximum, which happens when
the Crisian Sea is about f of its width, from the western limb of the
moon, is about 7° 30', and it altogether vanishes in perigee and apogee.
—En.

\ The moon is also Subject to two other kinds of libration, called the
diurnal libraiion andt'ies/i roidal libration.
H 4

152 OF THE SOLAR SYSTEM. Part II.

While the moon revolves round the earth in an ellip-
tical orbit, she likewise accompanies the earth in its ellip-
tical orbit round the sun : by this compound motion her
path is every where concave towards the sun.*

The moon, like the planets, is an opaque body, and
shines entirely by the light received from the sun, a portion
of which is reflected to the earth. As the sun can only
enlighten one half of a spherical surface at once, it follows
that according to the situation of an observer, with re-
spect to the illuminated part of the moon, he will see
more or less of the light reflected from her surface. At
the conjunction, or time of new moon, the moon is be-
tween the earth and the sun, and consequently that side
of the moon which is never seen from the earth is enlight-
ened by the sun ; and that side which is constantly turned
towards the earth is wholly in darkness, t Now, as the
mean motion of the moon in her orbit exceeds the apparent
motion of the sun by about 12° 11' in a dayj, it follows
that, about four days after the new moon, she will be seen
in the evening a little to the east of the sun, after he has
descended below the western part of the horizon. A spec-
tator will see the convex part of the moon towards the
west, and the horns or cusps towards the east; or if the
observer live in north latitude, as he looks at the moon

The diurnal libration arises from the somewhat different views a
spectator on the earth's surface obtains of the moon at the time of her
rising, culminating, and setting, and is therefore dependent on the mo-
tion of the observer about the centre of the earth ; for it is easy to con-
ceive, and observation proves, that at the time of the moon's rising,
certain spots are visible about the upper limb, which disappear as she
advances to the meridian, while others about the opposite limb of the
moon, not before observable, come into view as she approaches
towards and descends below the western verge of the horizon.

The spheroidal libration is caused by the action of the earth on the
elevated parts of the lunar spheroid, whereby a small vibratory motion
of the moon is produced about an axis, perpendicular to the radius
vector, or line joining the earth and moon. — ED.

* See M. Madaurin's account of Sir Isaac Newton's discoveries,
• book iv. chap. 5. ; Howe's Fluxions, second edition, page 225. ; Fer-
guson's Astronomy, octavo edition, article 266. ; or a Treatise on
Astronomy, by Dr. Olinthus Gregory, article 458.

t Except the light which is reflected upon it from the earth, which
we cannot perceive.

t See the note, page 82.

. V. OF THE SOLAR SYSTEM. 153

the horns will appear to the left hand ; for if the line join-
ing the cusps of the moon be bisected by a perpendicular
passing through the enlightened part of the moon, that
perpendicular will point directly to the sun. As the moon
continues her motion eastward, a greater portion of her
surface towards the earth becomes enlightened ; and when
she is 90 degrees eastward of the sun, which will happen
about ?-£ days from the time of new moon, she will come
to the meridian about 6 o'clock in the evening, having
the appearance of a bright semi-circle ; advancing still to
the eastward, she becomes more enlightened towards the
earth, and at the end of about 14^ days, she will come to
the meridian at midnight, being diametrically opposite to
the sun ; and consequently she appears a complete circle,
or it is said to be full moon. The earth is now between
the sun and the moon, and that half of her surface which is
constantly turned towards the earth is wholly illuminated
by the direct rays of the sun ; whilst that half of her
surface which is never seen from the earth is involved in
darkness. The moon continuing her progress eastward,
she becomes deficient on her western edge, and about 7-£
days from the full moon she is again within 90 degrees of
the sun, and appears a semi-circle with the convex side
turned towards the sun: moving on still eastward, the
deficiency on her western edge becomes greater, and she
appears a crescent, with the convex side turned towards
the east, and her cusps or horns turned towards the west ;
and about 14^ days from the full moon she has again
overtaken the sun, this period being performed in 29 days
12 hours 44 minutes 3 seconds, as has been observed
before. Hence, from the new moon to the full moon, the
phases are homed, half-moon, and gibbous; and as the
convex or well defined side of the moon is always turned
towards the sun, the horns or irregular side will appear to
the east, or towards the left hand of a spectator in north
latitude. From the full moon to the change, the phases
are gibbous, half-moon, and horned ; the convex or well-
defined side of her face will appear to the east, and her
horns or irregular side towards the west, or to the right
hand of a spectator.

As the full moons always happen when the moon is
H 5

] 54- OF THE SOLAR SYSTEM. Part II.

directly opposite to the sun, all the full moons in our
winter happen when the moon is on the north side of the
equinoctial. The moon, while she passes from Aries to
Libra, will be visible at the north pole, and invisible
during her progress from Libra to Aries ; consequently,
at the north pole, there is a fortnight's moonlight and a
fortnight's darkness by turns. The same phenomena will
happen at the south pole during the sun's absence in our
summer. If the earth, the moon, and the sun were in all
the same plane, there would be an eclipse of the sun at
every new moon (for then the moon is between the earth
and the sun), and there would be an eclipse of the moon
at every full moon, at which time the earth is between
the sun and the moon. But as the orbit of the moon
crosses the orbit of the earth or the ecliptic in two oppo-
site points called the nodes, it is evident that the moon is
never in the ecliptic except when she is in one of these
nodes ; an eclipse, therefore, can never happen unless the
moon be in or near one of these nodes ; at all other times
she is either above or below the orbit of the earth ; and
though the moon crosses each of these nodes every month,
yet if there should not be a new or full moon, at or near
that time, there will be no eclipse. (See more of this sub-
ject in a succeeding chapter.') The influence of the moon
upon the waters of the ocean has already been explained;
and the nature of the harvest-moon will be shown amongst
the problems on the globes.

The moon's greatest horizontal parallax is 61' 32", the
least 54?' 4", consequently the mean horizontal parallax
is 57" 4<8" * ; and her mean distance from the earth
236847 miles, t The apparent diameter of the moon is
variable according to her distance from the earth; her
mean apparent diameter is stated to be 31' 7"J; hence

* Dr. Hutton's Mathematical Diet, word Parallax.
| As in the note, page 68.

Sine of angle PSO 57' 48" 8-2256335

Is to semi-diameter of the earth PO 0-0000000

As radius, sine of 90° = sine OPS 10-0000000

Is to 59-47938 semi-diameters, 1-7743665

Hence 59-47938x3882 = 236846-89 miles, distance of the moon
from the earth.

\ Kince's Astronomy. JFoodfiouse's Astronomy, page 314.

Chap. V. OF THE SOLAR SYSTEM. 155

her real diameter is 2144? miles *, and her magnitude
about -^Q of the magnitude of the earth. The moon per-
forms her revolution round the earth in 27 days 7 hours
4-3 minutes 5 seconds, as has been observed before, con-
sequently she travels at the rate of 2270 f miles per hour
round the earth, besides attending the earth in its annual
journey round the sun.

The surface of the moon is greatly diversified with in'
equalities, which through a telescope have the appearance
of hills and valleys. Astronomers have drawn the face of
the moon as viewed through a telescope, distinguishing
the dark and shining parts by their proper shades and
figures. Each of the spots on the moon has been marked
by a numerical figure, serving as a reference to the proper
name of the particular spot which it represents ; as, ^
Herschel's volcano; 1, Grimaldi; 2, Galileo, &c. ; so that
the several spots are named from the most noted astro-
nomers, philosophers, and mathematicians. The best
and most complete picture of the moon is that drawn on
Mr. Russel's lunar globe. £

Dr. Herschel informs us that, on the 19th of April,

* As in the preceding notes say, inversely, 59-47938 semi-diam. :
31' 7" :: 23882-84 sem. : 4//<6497, the apparent diameter of the moon
at a distance from the earth equal to that of the sun; hence 32' 2" :
886149 :: 4".6497 : 2143-8 miles, the diameter of the moon. Or, by
trigonometry, the angle mon, (Plate IV. Fig. 3.) = 31' 7", hence

IcrvO QI / 7»

omn= g3 - = 89°59'44»26'"i

Sine of 89° 59' 44*, &c, = (sine of 90 nearly) 10-OOOOOOO

Is to 59-47938 semi-diameters 1-7743665

As sine 31' 7" 7-9567310

Is to -53839 semi-diameters of the earth 1-7310975

And -53839 x 3982 = 2143-86, &c. miles the diameter of the moon :
See the notes, page 142. If the cube of the earth's diameter be di-
vided by the cube of the moon's diameter, the quotient will be 51*2 ;
hence the magnitude of the earth is upwards of 50 times that of the
moon.

t For, by the note, page 146.; 113: 355: 1236846 -9 x 2 : 1488153-09
miles circumference of the moon's orbit; then 27 d. 7h. 43m. 5 sec.
: 1488r53-09 m. : : 1 h. : 2269-5 miles.

t The representation of the moon, Plate 7. (copied from my Astro-
nomicon), will, it is presumed, be found as correct as the scale upon
which it is drawn wiU possibly admit. — En.
H 6

156 OF THE SOLAR SYSTEM. Part II.

1787, he discovered three volcanoes in the dark part of
the moon ; two of them appeared nearly extinct, the
third exhibited an actual eruption of fire, or luminous
matter. On the subsequent night it appeared to burn
with greater violence, and might be computed to be
about three miles in diameter. The eruption resembled
a piece of burning charcoal, covered by a thin coat of
white ashes ; all the adjacent parts of the volcanic moun-
tain were faintly illuminated by the eruption, and were*
gradually more obscure at a greater distance from the
crater. That the surface of the moon is indented with
mountains and caverns, is evident from the irregularity
of that part of her surface which is turned from the sun :
for, if there were no parts of the moon higher than the
rest, the light and dark parts of her disc at the time of
the quadratures would be terminated by a perfectly
straight line; and at all other times the termination
would be an elliptical line, convex towards the enlight-
ened part of the moon in the first and fourth quartei'Sj
and concave in the second and third ; but instead of
these lines being regular and well defined when the
moon is viewed through a telescope, they appear notched
and broken in innumerable places. The edge of the moon,
which is turned towards the sun, is regular and well de-
fined, and at the tjme of full moon no notches or indented
parts are seen on her surface. In all situations of the
moon, the elevated parts are constantly found to cast a tri-
angular shadow with its vertex turned from the sun ; and,
on the contrary, the cavities are always dark on the side
next the sun, and illuminated on the opposite side : these
appearances are exactly conformable to what we observe
of hills and valleys on the earth ; and even in the dark
part of the moon's disc, near the borders of the lucid sur-
face, some minute specks have been seen, apparently
enlightened by the sun's rays : these shining spots are
supposed to be the summits of high mountains *, which

* Supposing this to be the fact, astronomers have determined the
height of some of the lunar mountains. The method made use of
by Riccioli (though it gives the true result only at the time of the
quadratures) is here explained, because it is much more simple than
the general method given by Dr. Herschel in the Philosophical Trans-

Chap.V. OF THE SOLAR SYSTEM. 157

are illuminated by the sun, while the adjacent valleys
nearer the enlightened part of the moon are entirely dark.
Whether the moon has an atmosphere or not, is a
question that has long been controverted by various
astronomers* : some endeavour to prove, that the moon
has neither an atmosphere, seas, nor lakes ; while others
contend that she has all these in common with our earth,
though her atmosphere is not so dense as ours. The moon
is known to have mountains and valleys like our earth,
and appears nearly the same with respect to shape, and

actions for 1780. Let ADB (Plate IV. Fig. 7.) be the disc or face of
the moon at the time of the quadratures, ACS the boundary of light
and darkness ; MO a mountain in the dark part, the summit M of
which is just beginning to be enlightened, by a ray of light SAM from
the sun. Now, by means of a micrometer, the ratio of MA to
AB may be determined ; and as AC is the half of AB, and MAC
a right-angled triangle by Euclid 1 and 47th A/AC* + AM2=oi,
from which take co = AC, and the remainder MO is the height of the
mountain. Riccioli observed the illuminated part of the mountain
St. Catherine, on the fourth day after the new moon, to be distant
from the illuminated part of the moon about 1-sixteenth part of the
moon's diameter, viz. MA = 1-sixteenth of AB, or = 1-eighth of AC ;
now, if we take the moon's diameter 2144 miles, as we have before
determined, the height of this mountain will be 8-$ miles ! Galileo
makes MA = l-20th of AB ; and Hevelius makes MA = l-26th of
AB ; the former of these will give the height of the mountain 5^0
miles, and the latter 3-jg miles. Dr. Herschel thinks, " that the
heights of the lunar mountains are in general greatly over-rated, and
that the generality of them do not exceed half a mile in their perpen-
dicular elevation." On the contrary, M. Schroeter says, that there
are mountains in the moon much higher than any on the earth, and
mentions one above a thousand toises higher than Chimbora9O in South
America. The same author makes some of the mountains of Venus
upwards of twenty-three thousand toises in height, which is above seven
times the height of Chimboraco.

* The observations of Schroeter, however, seem to have decided
this controversy by the complete discovery of the lunar atmosphere.
This accurate observer at length succeeded in detecting a faint glim,
raering light stretching from the points of the horns into the dark
hemisphere. From the breadth of this crepuscular light he has com-
puted that the utmost height of the lunar atmosphere, where it could
affect the brightness of a fixed star, or inflect the solar rays, does
not exceed 5742 English feet, which space subtending at our earth an
angle of only 0. 94 seconds will be passed over by a star in two seconds
of time. — ED,

158 OF THE SOLAR SYSTEM. Part II.

the nature of her motions. Reasoning, therefore, by ana-
logy, we may fairly infer that she resembles it in other
respects.

V. OF MARS $.

Mars appears of a dusky red colour, and though he is
sometimes apparently as large as Venus, he never shines
with so brilliant a light. From the dulness and ruddy
appearance of this planet, it is conjectured that he is
encompassed with a thick cloudy atmosphere, through
which the red rays of light penetrate more easily than
the other rays. This being the first planet without the
orbit of the earth, he exhibits to the spectator different
appearances to Mercury and Venus. He ,is sometimes in
conjunction with the sun, like Mercury and Venus, but
was never known to transit the sun's .disc. Sometimes
he is directly opposite to the sun, that is, he comes to the
meridian at midnight, or rises when the sun sets, and
sets when the sun rises ; at this time he shines with the
greatest lustre, being nearest to the earth. Mars, when
viewed through a telescope, appears sometimes full and
round, at others gibbous, but never horned; clearly showing
that Mars moves in an orbit exterior to that of the earth.
The apparent motion of this planet, like that of Mercury
and Venus, is sometimes direct, at others retrograde, and
sometimes he appears stationary. Sometimes he rises before
the sun, and is seen in the morning ; at others he sets after
the sun, and of course is seen in the evening. Mars re-
volves on its axis * in 24? hours 39 minutes 21 seconds ;
and its polar diameter is to its equatorial diameter as 15
to 16, according to Dr. Herschel; but Dr. Maskelyne,
who carefully observed this planet at the time of opposi-
tion, could perceive no difference between its axis. The
inclination of the orbit of Mars to the plane of the eclip-
tic is 1° 5V; the place of his ascending node about 18°
in Taurus f ; his horizontal parallax is said to be 23"-8 ;
he performs his revolution round the sun in 1 year 321

* The axis of Mars is inclined to the ecliptic at an angle of about
30° 1 8' — ED.

f The longitude of the ascending node of Mars for the beginning of
the year 1750 was 17° 38' 38" in Taurus, and its variation in 100 years
is 46' 40". Vince's Astronomy. Consequently the longitude of his as-
cending node in 1850 will be 48° 25' 18", or 18° 25' 18" in Taurus.

Chap. V. OF THE SOLAR SYSTEM. 159

days 23 hours 15 minutes 44 seconds; and his apparent
semi-diameter, at his nearest distance from the earth, is
25"; consequently his mean distance from the sun is
144907630* miles; his diameter 4218 miles ; and his mag-
nitude a little more than jth of that of the earth.f This
planet travels round the sun at the rate of 55223 miles
per hour^.\ and the parallax of the earth's annual orbit,
as seen from Mars, is about 41 degrees. As the dis-
tances of the interior planets from the sun are found
by their elongations, so the distances of the exterior
planets may be found by the parallax of the earth's annual
orbit.$

* For, 686 days 23 hours 15min. 44 sec. =59354144 seconds, the
square of which is 3522914409972736, this divided by 995839704797184
the seconds in a year (see the note, page 141.), gives 3 '537632, the
cube root of which is 1 '523716, the relative distance of Mars from the
sun. Hence 1 '52371 86 x 23882-84 = 36390.6654 distance of Mars
from the sun in semi-diameters of the earth, and 36390'6654 x 3982
= 1 44907629.6 miles, the mean distance of Mars from the sun. Now,
if the horizontal parallax of Mars at the time of opposition be 25 '.6,
as stated by M. de la Caille, we have (see Plate IV. Fig. 6.)

Sine PSO <= sine 23"'6 G'0583927

Is to PO = 1 semi-diameter O'OOOOOOO

As radius sine of 90° lO'OOOOOOO

Is to so = 8741*93 semi-diameter ... 3'9416073
Hence the distance of Mars from the earth, at the time of opposition-,
is 874 1-93 of the earth's semudiameters ; 8741-93 : 25" : : 23882-84 :
9'' -15 the apparent diameter of Mars if seen from the earth at a dis-
tance equal that of the sun ; then 32' '2" : 886149 : : 9'/'15 : 4218
miles the diameter of Mars.

t The cube of 7964, the diameter of the earth, is 505119057344 ;
and the cube of 4218, the diameter of Mars, is 75044648232 ; the
quotient produced by dividing the former by the latter, is 6-73. viz. the
magnitude of the earth is nearly seven times that of Mars.

\ For, 113 . 355 : : J 44907630 x 2 : 910481569 miles, the cir-
cumference of the orbit of Mars, and 686 days 23 h. 15 min. 44 sec.
910481569 m. : : 1 h. : 55223 miles.

§ In Plate IV. Fig. 8. let s represent the sun, E the earth, and M
Mars ; now, as the earth moves quicker in its orbit than Mars, the
planet Mars will appear to go backward when the earth passes it.
Thus, when the earth is at E, Mars will appear among the fixed stars
at m ; but as the earth passes from E to e, Mars will appear to go
from m to n, though he is in reality travelling the same way as the
earth from M to o. The place m, where Mars is seen from the earth
among the fixed stars, is called his GEOCENTRIC place, but the place

160 OF THE SOLAR SYSTEM. Part II.

VI. OF VESTA g.

This planet was discovered by Dr. Oilers of Bremen,
on the 29th of March, 1807 ; .its distance from the sun is
225435000* miles; the length of its year is 13257 days.
The inclination of its orbit to the plane of the ecliptic,
7° 8' 9". Vesta appears like a star of the fifth magnitude.

VII. OF JUNO f.

Juno was discovered by Mr. Harding of Lilienthal,
in the duchy of Bremen, on the 1st of September, 1804.
It appears like a star of the eighth magnitude ; its distance
from the sun is 253380485 miles, and its periodical revo-
lution is performed in 1592-66 days. Inclination of its
orbit to the plane of the ecliptic, 13° 4' 9"'7.

VIII. OF CERES ?.'

Ceres was discovered by M. Piazzi, astronomer royal,
at Palermo, in the island of Sicily, on the 1st of January,
1801. The length of its year is 4 years 221 days
13 hours; its distance from the sun is 262903570 miles;
and its diameter, according to Dr. Herschel, is about
162 miles. Ceres appears like a star of the eighth mag-
nitude. Its orbit is inclined to the plane of the ecliptic
in an angle of 10° 37'26"»2.

r, where he would be seen from the sun, is called his HELIOCENTRIC
place, and the arc m r, which is the difference between his apparent
and true place, is called the PARALLAX OF THE EARTH'S ANNUAL
ORBIT. Now, as this angle may be determined from observation,
and is known to be about 41° ; in the right-angled triangle SEM, we
have given SE = 23882-84 semi-diameters, the'distance of the earth
from the sun, the angle SMB measured by the arc m r = 41°, to find
SM = 36403 '49 semi- diameters of the earth, the distance of Mars from
the sun. According to M. Laplace, the sidereal revolution of Mars
is performed in 686 '9 7 96 19 days, and his mean distance from the sun
is 1 -523694.

* Mean distance 2-373. The mean distance of Juno is 2-667163,
of Ceres 2-767406, of Pallas 2*767592 according to Laplace, and the
periods which are given from the same author are sidereal periods.

Chap. V. OF THE SOLAR SYSTEM. 161

IX. OF PALLAS 2 •

Pallas was discovered by Dr. Others, on the 28th of
March, 1802. The length of its year is 1 686-54- days;
and its distance from the sun 262921240 miles. Pallas
appears like a star of the seventh magnitude, and its
diameter is stated to be about 1 10 miles. Its orbit is
inclined to the plane of the ecliptic in an angle of
S4° 34/ 55".

X. OF JUPITER If , and his Satellites, fyc.

Jupiter is the largest of all the planets, and notwith-
standing his great distance from the sun and the earth,
he appears to the naked eye almost as large as Venus,
though his light is something less brilliant. Jupiter,
when in opposition to the sun, (that is, when he comes to
the meridian at midnight, or rises when the sun sets, and
sets when the sun rises,) is much nearer to the earth than
he is a little before and after his conjunction with the
sun ; hence, at the time of opposition, lie appears larger
and more luminous than at other times. When the lon-
gitude of Jupiter is less than that of the sun, he will be a
morning star, and appear in the east before the sun rises ;
but, when his longitude is greater than the sun's longi-
tude, he will be an evening star, and appear in the west
after the sun sets. Jupiter revolves on his axis in 9 hours
56 minutes, which is the length of his day ; but as his
axis is nearly perpendicular to the plane of his orbit, he
has no diversity of seasons. Jupiter is surrounded by
faint substances called zones or belts ; which, from their
frequent change in number and situation, are generally
supposed to consist of clouds. One or more dark spots
frequently appear between the belts; and when a belt
disappears, the contiguous spots disappear likewise. The
time of the rotation of the different spots is variable,
being less by six minutes near the equator than near the
poles. Dr. Herschel has determined, that not only the
times of rotation of the different spots vary, but that the
time of rotation of the same spot (between the 25th of
February 1773 and the 12th of April) varied from 9

162 OF THE SOLAR SYSTEM. Part II.

hours 55 minutes 20 seconds, to 9 hours 51 minutes
35 seconds.

The inclination of the orbit of Jupiter to the plane of
the ecliptic is 1° 18" 51"'3; the place of his ascending node
about 8 degrees in Cancer* ; and he performs his revolu-
tion round the sun in 11 years 315 days 14- h. 27 m. 11 sec.,
moving at the rate of 29894- miles per hour, his mean
distance from the sun being 4944-99108 miles. -j- Jupiter,
at his mean distance from the earth, at the time of oppo-
sition, subtends an angle of 46", hence his real diameter
is 89069 miles J ; and his magnitude 1400 times that of
the earth. § The light and heat which Jupiter receives
from the sun is about JT of the light and heat which the
earth receives. ||

On account of the great magnitude of Jupiter, and his
quick revolution on his axis, he is considerably more

* The place of Jupiter's ascending node for the beginning of the
year 1750 was 7° 55' 32" in Cancer, and its variation in 100 years is
59' 30". Consequently the longitude of his ascending node in 1850
will be 98° 55' 2", or 8° 55' 2" in Cancer.

f For, 4330 days 14 h. 27 min. 11 sec. = 374 164031 seconds,
the square of which is 139998722094168961 ; this divided by995839
704797184, the square of the seconds in a year (see the note, page 141.)
gives 140'5835913, the cube root of which is 5'1997, the relative
distance of Jupiter from the sun. Hence 23882-84 x 5'1997 =
1241 83 '6031 48 distance of Jupiter from the sun in semi-diameters of
the earth; and 124183-603148 x 3982 = 494499107-7 miles, the
mean distance of Jupiter from the sun. According to Laplace the
sidereal period of Jupiter is 4332-596308 days, and his mean distance
from the sun 5-202791

Now (by the note, page 143.), 113 : 355 :: 494499107*7 x 2 :
3107029791 miles, the circumference of the orbit of Jupiter, and
4330 d. 14 h. 27 min. 11 sec. : 3107029791 II 1 h. : 29894 miles.

\ 494499108 — 95101468 miles, the distance of the earth from the
sun, = 399397640, distance of the earth from Jupiter. Now, by the
rule of three inversely, 399397640 : 46" :: 95101468 : 193//>1862.
the apparent diameter of Jupiter at a distance from the earth equal to
that of the sun. Hence (as in the note, page 142.), 32' 2" I 886149
I; 193"-1862 : 89069-5 miles, the diameter of Jupiter.

§ For, if the cube of the diameter of Jupiter be divided by the cube
of the diameter of the earth, the quotient will be 1398*9= 1400 nearly.

|| If the square of the mean distance of Jupiter from the sun be
divided by the square of the mean distance of the earth from the
sun the quotient will be 27.

Chap. V.

OF THE SOLAR SYSTEM.

163

flatted at the poles than the earth is. The ratio between
his polar and equatorial diameters, has been differently
stated by different astronomers : Dr. Pound makes it as 12
to 13; Mr. Short, as 13 to 14; Dr. Bradley, as 12£ to
13i ; and Sir Isaac Newton (by theory) 9i to 10^.

Of the Satellites of Jupiter.

Jupiter is attended by four satellites or moons, each of
which revolves round him in a manner similar to that of
the moon round the earth. The times of their periodical
revolutions round Jupiter, and their respective distances
from his centre, are given in the following table : *

Satellites.

Periodical revolution.

Distance from
Jupiter in semi-
diameters.

Distance from
Jupiter in
English miles.

I.
II.
III.

IV.

d. h. m. sec.

1 .18.27.33
3.13.13.4-2
7. 3.4-2.33
16.16.32. 8

5-67
9-00
14-38
25-30

252510
400810
640406
1126723

The satellites of Jupiter are invisible to the naked eye;
they were first discovered by Galileo, the inventor of
telescopes, in the year 1610. This was an important dis-
covery ; for, as these satellites revolve round Jupiter in
the same direction which Jupiter revolves round the sun,
they are frequently eclipsed by his shadow, and afford
an excellent method of finding the true longitudes of

* The second and third columns in the above table are copied
from M. de la Lande, and the fourth is found by multiplying the
numbers in the third column by 44534-5, being the half of 89069,
the diameter of Jupiter. The distances of the satellites from the centre
of Jupiter may be found at the time of their greatest elongations, by
measuring their distances from the centre of Jupiter, and also the di-
ameter of Jupiter with a micrometer. Then say, as the apparent
diameter of Jupiter (by the micrometer) is to his real diameter, so is
the apparent distance of the satellite to its real distance. Or having
determined the periodical times of the satellites, and the distance of
one of them from the sun, the distances of all the rest may be found by
Kepler's rule, as in page 144.

164 OF THE SOLAR SYSTEM. Part II.

places on the land. To these eclipses we likewise owe
the discovery of the progressive motion of light, and
hence the aberration of the fixed stars.

The satellites of Jupiter do not revolve round him in
the same plane, neither are their nodes in the same
place. These satellites appear of different magnitudes
and brightness, the fourth generally appears the smallest,
but sometimes the largest, and the apparent diameter of
its shadow on Jupiter is sometimes greater than the satel-
lite. M. Cassini and Mr. Pound supposed that the satel-
lites of Jupiter revolved on their axes ; and Dr. Herschel
has discovered that they revolve about their axes in the
time in which they respectively revolve about Jupiter.

The first satellite is the most important of the four,
from its numerous eclipses. The times of the eclipses of
the satellites of Jupiter are calculated for the meridian of
Greenwich, and inserted in the XXth page of the Nautical
Almanac for every month, and their appearances, with
respect to Jupiter, are inserted in page XIX. As the
earth turns on its axis from west to east at the rate of 15
degrees in an hour, or one degree in four minutes of time,
a person one degree westward of Greenwich will observe
the immersion or emersion of any one of the satellites
of Jupiter four minutes later than the time mentioned
in the Nautical Almanac ; and, if he be one degree east-
ward of Greenwich, the eclipse will happen four minutes
sooner at his place of observation than at Greenwich.
These eclipses must be observed with a good telescope and
a pendulum clock which beats seconds or half-seconds.

The configurations of the satellites of Jupiter at half-

5ast three o'clock in the morning of part of the month of
une, and in the year 1845, are given in the XlXth page of
the Nautical Almanac as in the following page.

" This table represents at 15 h. 30 m. after mean noon,
or half past 3 o'clock of the following morning to that of
which the date is given, of each day of the month, the
relative positions of the images of Jupiter and his satel-
lites, as they would appear (disregarding their latitudes)
in an inverting telescope. Jupiter is indicated by the
white circle (O) in the centre of the page, the satellites
by points. The numerals 1, 2, 3, and 4-, annexed to the
points, serve to distinguish the satellites from each other ;

Chap. V.

OF THE SOLAR SYSTEM.

165

and their positions are such as to indicate the directions
of the satellites' motions, which are to be considered, in
all cases, as towards the numerals. When a satellite is at
its greatest elongation, the point is placed above or below
the. centre of the numeral. A white circle, as (O)> at the
left or right hand of the page, denotes that the satellite
placed by the side of it is on the disc of Jupiter; and a
black circle ( • ), that it is either behind the disc or in the
shadow of Jupiter." .

*£**] West. East.

>-o o A- »• !

»-o *-o" -* i

3. .2 1. O 4-

•» O :«l

•S.lQ 2. 4-

»• O >!

:*O *• .3

Ql. 4. .2 3.

"• 4. SO'3'

3; '-O. 1

4. -3 Q.« -1

4- .3 l. Q 2.

•4 . 2. O -3 1-

" If an inverting telescope be directed towards Jupiter
on June 28. 1845, at 15 h, 30 m. mean time, the satellites
will appear to an observer at Greenwich in the positions
as laid down in the table. The 1st and 2d satellites which
are really to the left of the planet, will appear to the right
of it, and the 3d and 4th, which are really to the right,
will appear to be to the left."

" West and East, at the head of the table, are inserted to
show the positions of the satellites with respect to Jupiter,
as they would appear in a telescope that does not invert.
Jupiter being always to the south of the zenith of Green-
wich, the satellites which are here laid down on the left
of Jupiter would appear to the West, and those on the
right hand to the East of the planet."

"As regards their positions to the east or west, the table
viewed directly exhibits the satellites in an inverted order ;

166 OF THE SOLAR SYSTEM. Part II.

but if the leaf be turned over, and the page viewed from
the other side, they will appear in their real positions."

By observations on the satellites of Jupiter the progres-
sive motion of light was discovered ; for it has been found
'by repeated experiments, that, when the earth is exactly
between Jupiter and the sun, the eclipses of Jupiter's satel-
lites are seen 8^ minutes sooner than the time predicted
by calculating from astronomical tables, truly constructed;
and when the earth is nearly in the opposite point of its
orbit, these eclipses happen about 8^ minutes later than the
time predicted; hence it is inferred that light takes up about
16^ minutes of time to pass over a space equal to the dia-
meter of the earth's annual orbit, which is 190 millions of
miles, or double the distance of the earth from the sun; for
if the effects of light were instantaneous, the eclipses of the
satellites would in all situations of the earth in its orbit
happen exactly at the time predicted by calculation.

OF SATURN 1? , his Satellite and Ring.

Saturn shines with a pale, feeble light, being the farthest
from the sun of any of the planets that are visible without
a telescope. This planet, when viewed through a good
telescope, always engages the attention of the young astro-
nomer by the singularity of its appearance. It is sur-
rounded by an interior and exterior ring, beyond which
are seven satellites or moons, all, except one, in the same
plane with the .rings. These rings and satellites are all
opaque and dense bodies, like that of Saturn, and shine
only by the light which they receive from the sun. The
disc of Saturn is likewise crossed by obscure zones "or
belts, like those of Jupiter, which vary in their figure ac-
cording to the direction of the rings. Saturn performs
his revolution round the sun in 29 years 174- days 1 hour
.*>! minutes 11 seconds*; hence his mean distance from
the sun is 907089032 miles f ; and his progressive motion
in his orbit is 22072 miles per hour.

* Laplace states the sidereal period of Saturn to be 10758-96984
days, and his mean distance from the sun 9'53877 ; see also Abrcge
(V Astronomic, par M. Delambre, page 452. Paris, 1813.

f For 10759 d. 1 hr. 51 min. 1 1 sec. = 929584271 seconds, the square
of which is 864126916890601441, this divided by 995839704797184,

Chap. V. OF THE SOLAR SYSTEM. 167

The inclination of the orbit of Saturn to the plane of
the ecliptic is said to be 2° 29' 35*7, and the place of his
ascending node about 22 degrees in Cancer. *

Saturn, at his mean distance from the earth, subtends
an angle of 20" ; hence his real diameter is 78730 f miles,
and his magnitude 966 J times that of the earth. The
light and heat which this planet receives from the sun is
about — !— part § of the light and heat which the earth
receives.

According to Dr. Herschel, Saturn revolves on his axis
from west to east in 10 hours 16 min. 2 sec. and this axis
is perpendicular to the plane of his ring. The equatorial
diameter of Saturn, viz. the diameter in the direction of
the ring, is to the polar diameter, viz. the axis, as 11 to 10.

Of the Satellites of Saturn.

Saturn is attended by seven moons ; the fourth was dis-
covered by Huygens, a Dutch mathematician, in the
year 1655. The first, second, third, and fifth were dis-
covered at different times, between the years 1671 and

the square of the seconds in a year (see the note, page 144.) gives
867.736958, the cube root of which is 9.538 118, the relative distance of
Saturn from the sun. Hence 23882.84 x 9.53118 = 227797.34609512,
distance of Saturn from the sun in semi-diameters of the earth ; and
227797.34609ol2 x 3982 = 907089032.15 miles, the mean distance of
Saturn from the sun. 113 : 355 : : 907089032 x 2 : 5699408962.1238
miles circumference of the orbit of Saturn. Then,
10759 d. 1 h. 51 m. 11 sec. : 5699408962 miles : : 1 h. : 22072
miles which Saturn moves per hour in his orbit.

* The place of Saturn's ascending node for the beginning of the
year 1750 was 21° 32' 22" in Cancer, and its variation in 100 years is
55' 30". Vinces Astronomy.

f 907089032 — 95101468 miles, the distance of the earth from the
sun,=8 11 987564 miles distance of the earth from Jupiter. Now,
inversely, 811987564: 20" : : 95101468 : 170". 762, the apparent dia-
meter of Saturn at a distance from the earth equal to that of the sun
(by the note, page 145.) ; 32' 2" : 886149 : : 170".762 : 78730 miles,
the diameter of Saturn.

J Found by dividing the cube of the diameter of Saturn by the cube
of the diameter of the earth.

§ Found by dividing the square of the mean distance of Saturn
from the sun by the square of the earth's mean distance from the sun.

168

OF THE SOLAR SYSTEM.

PartlL

1685, by Cassini, a celebrated Italian astronomer. The
sixth and seventh satellites were discovered by Dr. Hers-
chel in the year 1787 and 1789. The two satellites dis-
covered by Dr. Herschel are nearer to Saturn than the
other five, and therefore should be called the first and
second ; but to distinguish them from the other satellites,
and to prevent confusion in referring to former observ-
ations, they are called the sixth and seventh satellites.
The seventh satellite, which is nearest to Saturn, was
discovered a short time after the sixth. In the following
table, the satellites are arranged according to their re-
spective distances from Saturn, and the Roman figures in
the left-hand column show the number of the satellite.
The figures between the parenthesis show the order in
which they ought to be numbered.

Satellites.

Periodical revolution.

Distance from
Saturn in
semi-diame-
ters, from La-
place.

Distance from
Saturn in En-
glish miles.

VII. (1)
VI. (2)
I. (3).
II. (4)
III. (5)
IV. (6)
V. (7)

d. h. m. sec.
0 . 22 . 37 . 23
1 . 8 . 53 . 9
1.21.18.27
2.17.44.51
4.12.25.11
15.22.41.16
79. 7.53.43

3.080
3.952
4.893
6.268
8.754
20.295
59.154

121244
155570
192613
246740
344601
798912
2328597

The first, second, third, and fourth satellites, as well as
the sixth and seventh, are all nearly in the same plane
with Saturn's ring, and are inclined to the orbit of Saturn
in an angle of about 30 degrees ; but the orbit of the
fifth satellite is said to make an angle of 15 degrees with
the plane of Saturn's ring. Sir Isaac Newton conjec-
tured * that the fifth satellite of Saturn revolved round its
axis in the same time that it revolved round Saturn ;
and the truth of his opinion has been verified by the ob-
servations of Dr. Herschel.

* Principia, Book III. Prop. xvii.

. V. OF THE SOLAR SYSTEM. 169

Of Saturn's Ring.

The ring of Saturn is a thin, broad, and opaque circular
arch, surrounding the body of the planet without touch-
ing it, like the wooden horizon of an artificial globe. If
the equator of the artificial globe be made to coincide
with the horizon, and the globe be turned on its axis from
west to east, its motion will represent that of Saturn on
its axis, and the wooden horizon will represent the ring ;
especially if it be supposed a little more distant from the
globe. The ring of Saturn was first discovered by Huygens,
and when viewed through a good telescope appears
double. Dr. Herschel says, that Saturn is encompassed
by two concentric rings, of the following dimensions : —

Miles.

Inner diameter of the smaller ring - - 146345

Outside diameter of ditto - - 184393

Inner diameter of the larger ring - - 190248

Outside diameter of ditto - - 204883

Breadth of the inner ring — - - 20000

Breadth of the outer ring - 72OO

Breadth of the vacant space, or dark zone between

the rings . - - - * 2839

The ring of Saturn revolves round the axis of Saturn,
and in a plane coincident with the plane of his equator,
in 10 hours 32 min. 15.4? sec. The ring being a circle,
appears elliptical, from its oblique position; and it ap-
pears most open when Saturn's longitude is about 2 signs
17 degrees, or 8 signs 17 degrees. There have been
various conjectures relative to the nature and properties
of this ring.

* The following dimensions, which are much more correct than
the above, are given by SitiJs F. W. Herschel (Cab. Cyclo., art.
Astronomy) : —

Miles.

Exterior diameter of exterior ring - - 176418

Interior diameter of ditto - - 155272

Exterior diameter of interior ring - - 151690

Interior diameter of ditto - ... 117339

Equatorial diameter of the body - - 79160

Interval between the planet and interior ring - 19090
Interval of the rings - 1791

Thickess of the rings not exceeding - - 1OO

EDITOR.

170 OF THE SOLAR SYSTEM. Part II.

XII. OF THE GEORGIUM SIDUS, or HERSCHEL $,
and its Satellites.

The Georgian is the remotest of all the known planets
belonging to the solar system ; it was discovered at Bath
by Dr. Herschel on the 13th of March, 1781. This planet
is called by the English the Georgium Sidus, or Georgian^
a name by which it is distinguished in the Nautical
Almanac. It is frequently called by foreigners Herschel^
in honour of the discoverer. The royal academy of
Prussia, and some others, called it Ouranus, because the
other planets are named from such heathen deities as
were relatives : thus Ouranus was the father of Saturn,
Saturn the father of Jupiter, Jupiter the father of Mars,
&c. This planet, when viewed through a telescope of a
small magnifying power, appears like a star between the
6th and 7th magnitude. In a very fine clear night, in the
absence of the moon, it may be perceived, by a good eye,
without a telescope. Though the Georgium Sidus was
not known to be a planet till the time of Dr. Herschel,
yet astronomers generally believe that it has been seen
long before his time, and considered as a fixed star.

In so recent a discovery of a planet at such an immense
distance, the theory of its magnitude, motion, &c. must
be in some degree imperfect. Its periodical revolution
round the sun is said to be performed in 83 years 150 days
18 hours * : the ratio of its diameter to that of the earth
is as 4.32 .to 1 ; consequently its magnitude is upwards of
eighty times that of the earth.

The Georgian planet is attended by six satellites; their
periodical revolutions and times of discovery are as fol-
low:—

d. h. m. s.

I. or nearest, revolves in 5 21 25 0, discovered in 1798.

II- - 8 17 1 19, discovered in 1787.

III. - - 10 23 4 0, discovered in 1798.

IV. . _ 1311 5 li, discovered in 1787.

V. - 38 1 49 0, discovered in 1798.

VI. - - 107 16 40 0, discovered in 1798.

* According to Laplace, the sidereal period of the Georgian is
30688.71 2687 days, and its mean distance from the earth 19. 183305.

Chap. VI. ON COMETS. 171

All these satellites were discovered by Dr. Herschel ;
their orbits are said to be nearly perpendicular to the
ecliptic, and, what is more singular, they perform their
revolutions round the Georgian planet in a retrograde
order, viz. contrary to the order of the signs.

CHAPTER VI.

On the Nature of Comets ; the Elongations, Stationary
and Retrograde Appearance of the Planets ; and on the
Eclipses of the Sun and Moon.

I. ON COMETS.

THOUGH the primary planets already described, and
their satellites, are considered as the whole of the regular
bodies which form the solar system, yet that system is
sometimes visited by other bodies, called comets, which
are supposed to move round the sun in elliptical orbits. —
These orbits are supposed to have the sun in one focus,
like the planets ; and to be so very eccentric, that the
comet becomes invisible when in that part of its orbit
which is the farthest from the sun. It is extremely diffi-
cult to determine the exact period of a comet's return to
its perihelion, in consequence of the attractions of the
larger planets, by which the path of the comet is consider-
ably changed at each revolution, and all these changes or
perturbations, as they are called, must be computed from
the theory of gravitation.* Among all the different
comets that have appeared, the period of only one f of
them (Halley's) is known with any degree of accuracy,
viz. that which was observed in 1531, 1607, 1682, 1759,

* The latest writings on the subject of comets are M. Pingre's
Cometographie, in two vols. 4to., and Sir Henry Englefield's work,
entitled, " On the Determination of the Orbits of Comets." A well
written article on Comets may be seen in Dr. Rees's Cyclopaedia, with
the elements of ninety-seven of them, ani the names of the authors
who have calculated their orbits,

f The periods of several other comets have now been determined:
one by Professor Encke of Berlin, which completes its period in about
3£ years, and another by M. Biela, which describes its orbit in 2461
days. The last appeared in 1839, and will return in 1846: the
former was seen in March, 1842; and will be seen again in 1845.

I 2

172 OP THE ELONGATIONS, &C. Part II.

and 1835, being about 76 years. The comets, Sir Isaac
Newton * observes, are compact, solid, and durable bodies,
or a kind of Planets which move in very oblique and
eccentric orbits every way with the greatest freedom, and
preserve their motions for an exceeding long time, even
where contrary to the course of the planets. Their tail is
a very thin and slender vapour, emitted by the head or
nucleus of the comet when ignited or heated by the sun.

II. OF THE ELONGATIONS, &c. OF THE INTERIOR
PLANETS.

Let T, E, e, (Plate IV. Fig. 8.) represent the orbit of
the earth ; «, iv, v, x, /, #, /*, the orbit of an interior planet,
as Mercury or Venus, and s the sun.

Let T represent the earth, s the sun, and a Venus at the
time of her inferior conjunction; at this time she will
disappear like the new moon, because her dark side will
be turned towards the earth. While Venus moves from
a towards w she appears to the westward of the sun, and
becomes gradually more and more enlightened (having
all the different phases of the moon). When she arrives
at v, her greatest elongation, she appears half enlightened,
like the moon in her first quarter ; at this time she shines
very bright. f From her inferior to her superior con-
junction, viz. from her situation in that part of her orbit
which is directly between the earth and the sun as at a,
to her situation in that part of her orbit in which the sun
is between her and the earth ; she rises before the sun in
the morning, and is called a morning star. From her
superior to her inferior conjunction she shines in the even-
ing after the sun sets, and is then called an evening star.

From the greatest elongation of Venus when westward
of the sun, as at v, to her greatest elongation when east-
ward of the sun, as at ^, she will appear to go forward in
her orbit, and describe the arc VWHG amongst the fixed

* Many interesting particulars respecting the nature of comets, &c.
may be learned by referring to the latter end of the third book of New-
ton's Principia.

f Venus gives the greatest quantity of light to the earth when her
elongation is 39° 44'. Vince's Fluxions.

Chap. VI. OF THE INTERIOR PLANETS. 173

stars; but from g to v she will appear retrograde*, or
return to the point v in the heavens in the order GHWV.
For when Venus is at/, she will be seen amongst the fixed
stars at H, and when at g she will appear at G: when she
arrives at h she will again appear at H in the heavens.
Hence in a considerable part of her orbit between /and h,
and between w and x, she will appear nearly in the same
point amongst the fixed stars, and at these times is said
to be stationary.

When a planet appears to move from the neighbour-
hood of any fixed stars, towards others which lie to the
eastward, its motion is said to be direct; when it proceeds
towards the stars which lie to the west, its motion is retro-
grade ; and when it seems not to alter its position amongst
die fixed stars, it is said to be stationary.

If the earth stood still at T, the planet Venus would
seem to make equal vibrations from the sun each way,
forming the equal angles OTS and -ZJTS, each 47° 48', her
greatest elongation, and the stationary points would al-
ways be in the same place in the heavens ; but it must be
remembered that, while Venus is proceeding in her orbit
from a towards #, the earth is going forward from T to-
wards E ; hence the stationary points, and places of con-
junction and opposition, vary in every revolution.

What has been observed with respect to Venus, may be
applied with a little variation to Mercury.

III. OF THE STATIONARY AND RETROGRADE APPEAR-
ANCES OF THE EXTERIOR PLANETS.

Because the earth's orbit is contained within the orbit
of Mars, Jupiter, &c. they are seen in all sides of the
heavens, and are as often in opposition to the sun as in
conjunction with him. Let the circle in which T is situ-
ated (Plate IV. Fig. 8.) represent the orbit of the earth,
and that in which M is situated the orbit of Mars. Now,
if the earth be at T when Mars is at M, Mars and the sun
will be in conjunction, but if the earth be at t when Mars

* The stationary and retrograde appearances of the inferior planets
are neatly illustrated by a small orrery, made and sold by Messrs. W.
and S. Jones, Mathematical Instrument-makers, Holborn.

i 3

174 ON SOLAR AND LUNAR ECLIPSES. Part II.

is at M, they will be in opposition, viz. the sun will appear
in the east when Mars is in the west. If the earth stood
still at T, the motion of the planet Mars would always ap-
pear direct; but the motion of the earth being more rapid
than that of Mars, he will be overtaken and passed by the
earth. Hence Mars will have two stationary and one re-
trograde appearances. Suppose the earth to be at E when
Mars is at M, he will be seen in the heavens among the
fixed stars at m ; and for some time before the earth has
arrived at E, and after it has passed E, he will appear
nearly in the same point m, viz. he will be stationary. —
While the earth moves through the part E t e of its orbit,
if Mars stood still at M, he would appear to move in a
retrograde direction through the arc mprn, in the hea-
vens, and would again be stationary at n ; but if, during
the time the earth moves from E to e, Mars moves from M
to o, the retrogradation would be nearly m p r.

The same manner of reasoning may be applied to Jupi-
ter and all the superior planets.*

IV. ON SOLAR AND LUNAR ECLIPSES.
An eclipse ofthesun\ is occasioned by the dark body of
the moon passing between the earth and the sun, or by
the shadow of the moon falling on the earth at the place
where the observer is situated : hence all the eclipses of
the sun happen at the time of the new moon. Thus, let s
represent the sun (Plate II. Fig. 6.), m the moon between
the tarth and the sun, «EG& a portion of the earth's
orbit, e and/ two places on the surface of the earth. The
dark part of the moon's shadow is called the umbra,
and the light part the penumbra ; now, it is evident that

* The illustrations of the real and apparent motions, stations, &c.
of the planets, both superior and inferior, afforded by the Astronomicon,
are at once natural, correct, and familiar, and have the additional
recommendation of being perfectly original. — ED.

t There is no such thing, properly speaking ; the phenomenon de-
scribed under the name of an eclipse of the sun is an occultation, or
hiding, wholly or partially, of that luminary by the interposition of the
moon, which therefore deprives certain portions of the earth's surface
of the sun's light, thereby eclipsing those portions. The distinction be-
tween occulting and eclipsing is always observed in describing the phe-
nomena of Jupiter's satellites, and why it should not be observed in
this case I have yet to, learn. These phenomena are very familiarly
illustrated by the Astronomicon, and in a manner altogether original.
— ED.

Chap. VI. ON SOLAR AND LUNAR ECLIPSES. 175

if a spectator be situated in that paYt of the earth where
the umbra falls, that is between e and f, there will be
a total eclipse of the sun at that place ; at e and/ in the
penumbra there will be a partial eclipse ; and beyond the
penumbra there will be no eclipse. As the earth is not
always at the same distance from the moon, if an eclipse
should happen when the earth is so far from the moon
that the lines ve andcy cross each other before they
come to the earth, a spectator situated on the earth, in a
direct line between the centres of the sun and moon, would
see a ring of light round the dark body of the moon,
called an annular eclipse ; when this happens there can be
no total eclipse any where, because the moon's umbra does
not reach the earth. People situated in the penumbra
will perceive a partial eclipse.

According to M. de Sejour, an eclipse can never be an-
nular longer than 12 min. 24 sec., nor total longer than 7 min.
58 sec. If the moon be exactly in her node, the centre of
her shadow will pass over the centre of the earth's en-
lightened disc, and describe a diameter, if the moon has
latitude, the centre of her shadow will describe a chord on
the circular disc of the earth, varying in length according
to her latitude : hence, the duration of a solar eclipse de-
pends on the length of the line which the centre of her
shadow describes, the proximity of the place to the centre
of the earth's disc, and the velocity of the moon's motion.

As the sun is not deprived of any part of his light dur-
ing a solar eclipse, and the moon's shadow, in its passage
over the earth from west to east, only covers a small part
of the earth's enlightened hemisphere at once, it is evident
that an eclipse of the sun may be invisible to some of the
inhabitants of the earth's enlightened hemisphere, and a
partial or total eclipse may be seen by others at the same
moment of time.

An eclipse of the moon is caused by her entering the
earth's shadow, and consequently it must happen when she
is in opposition to the sun, that is, at the time of full moon,
when the earth is between the sun and the moon. Let
s represent the sun (Plate II. Fig. 6.), EG the earth,
and m the moon in the earth's umbra, having the earth
between her and the sun ; DEP and HGP the penumbra.
I 4

176 ON SOLAR AND LUNAR ECLIPSES. Part II.

Now, the nearer any part of the penumbra is to the um-
bra, the less light it receives from the sun, as is evident
from the figure ; and as the moon enters the penumbra
before she enters the umbra, she gradually loses her light
and appears less brilliant.

The duration of an eclipse of the moon, from her first
touching the earth's penumbra to her leaving it, cannot
exceed 5^ hours. The moon cannot continue in the
earth's umbra longer than 3| hours in any eclipse, neither
can she be totally eclipsed for a longer period than 1-|
hour.* As the moon is actually deprived of her light
during an eclipse, every inhabitant upon the face of the
earth who can see the moon will see the eclipse.

GENERAL OBSERVATIONS ON ECLIPSES.

If the orbit of the earth and that of the moon were
both in the same plane, there would be an eclipse of the
sun at every new moon, and an eclipse of the moon at
every full moon. But the orbit of the moon makes an
angle of about 5£ degrees with the plane of the orbit of
the earth, and crosses it in two points called the nodes ;
now astronomers have calculated that, if the moon .be less
than 17° 21' from either node, at the time of new moon,
the sun may be eclipsed ; or if less than 1 1° 34?' from
either node, at the full moon, the moon may be eclipsed ;
at all other times, there can be no eclipse, for the shadow
of the moon will fall either above or below the earth at the
time of new moon ; and the shadow of the earth will fall
either above or below the moon at the time of full moon.
To illustrate this, suppose the right-hand part of the
moon's orbit (Plate II. Fig. 6.) to be elevated above the
plane of the paper, or earth's orbit, it is evident that the
earth's shadow, at full moon, would fall below the moon ;
the left-hand part of the moon's orbit at the same time
would be depressed below the plane of the paper, and the
shadow of the moon, at the time of new moon, would fall
below the earth. In this case the moon's nodes would
be between E and «, and between G and 6, and there

• Emerson's Astronomy, sect. 7, page 339.

Chap.VI. ON SOLAR AND LUNAR ECLIPSES. 177

would be no eclipse, either at the full or new moon : but
if the part of the moon's orbit between G and b be elevated
above the plane of the paper, or earth's orbit ; the part
between E and a will be depressed, the line of the moon's
nodes will then pass through the centre of the earth and
that of the moon, and an eclipse will ensue.* An eclipse
of the sun begins on the western side of his disc, and ends
on the eastern ; and an eclipse of the moon begins on the
eastern side of her disc, and ends on the western.

NUMBER OF ECLIPSES IN A YEAR.

The average number of eclipses in a year is four, two
of the sun and two of the moon ; and as the sun and moon
are as long below the horizon of any particular place as
they are above it, the average number of visible eclipses
in a year is two, one of the sun and one of the moon ; the
lunar eclipse frequently happens a fortnight after the solar
one, or the solar one a fortnight after the lunar one.

The most general number of eclipses, in any year, is four ;
there are sometimes six eclipses in a year, but tJcere camwt
be more than seven, norfeiver than two.

The reason will appear, by considering that the sun
cannot pass both the nodes of the moon's orbit more than
once a-year, making four eclipses, except he pass one of
them in the beginning of the year ; in this case he may
pass the same node again a little before the end of the
year, because he is about 173f days in passing from one
node to the other, therefore he may return to the same
node in about 346 days which is less than a year, mak-

* If you draw the figure on card-paper, and cut out the moon, her
shadow and orbit, so as to turn on the line a E G b, &c. the above illus-
tration will be rendered more familiar.

*t" The moon's nodes have a retrograde motion of about 1 9^ degrees
in a year (see page 151), therefore the sun will have to move (180 —

194

— = )170j degrees from one node to the other. But it has been

shewn in a preceeding note (see page 1 5), that the sun's apparent
diurnal motion is about 59' in a day; hence 59': 1 day : : 17Oj°:
173 days,

I 5

178 OF THE CALENDAR. Part II.

ing six eclipses. As twelve lunations*, or 354? days from
the eclipse in the beginning of the year may produce a
new moon before the year is ended, which (on account
of the retrograde motion of the moon's node) may fall
within the solar limit, it is possible for seven eclipses to
happen in a year, five of the sun and two of the moon. —
When the moon changes in either node, she cannot be
near enough to the other node at the time of the next
full moon to be eclipsed, and in six lunar months after-
wards, or about 177 days, she will change near the other
node ; in this case there cannot be more than two eclipses
in a year, and both of the sun.

The ecliptic limits of the sun are greater than those of
the moon, and hence there will be more solar than lunar
eclipses, in the ratio of 17° 21' to 11° 34- ', or nearly of
3 to 2 ; but more lunar than solar eclipses are seen
at any given place, because a lunar eclipse is visible
to a whole hemisphere at once : whereas a solar
eclipse is visible only to a part, as has been observed
before, and therefore there is a greater probability of
seeing a lunar than a solar eclipse.

CHAPTER VII.
Of the Calendar.

THE CALENDAR is a distribution of time as accommo-
dated to the various uses of life, and contains the division
of the year into months, weeks, days, &c. distinguishing the
several festivals, and other remarkable days. The manner
of reckoning time now in use was instituted by Pope
Gregory in 1582, and adopted in England in 1752.

The Common Notes for the year, usually given in our
almanacs, are, The Cycle of (he Moon, or Golden Number :

* That is, 12 times 29 days 12 hours 44 min. 3 sec., or 354 days
8 hours 48 min. 36 sec.

Chap. VII. OF THE CALENDAR. 179

the Epact ; the Cycle of the Sun and the Dominical Letter ;
the Number of Direction ; and the Roman Indiction.*

I. The Cycle of the Moon is a period of 19 years, after
which the new and full moons fall on the same day of the
month as they did at the beginning of the period. Any
number of this period is called the Golden Number.

To find the Golden Number for any Year.

RULE. Add 1 to the given year, and divide the sum
by 19, the remainder is the Golden Number. If there be
no remainder, the Golden Number is 19.

Example. What is the Golden Number for the year
1845?

(1845 + 1) -s- 19 leaves a remainder of 3, which there-
fore is the Golden Number.

II. The Epact for any Year is the moon's age at the
beginning of that year ; that is, the number of days which
have elapsed since the last new moon in the preceding
year. Its use is to find the Paschal full moon.

To find the Epact for any Year till 1900.

RULE. Find the Golden Number and subtract 1 from
it, multiply the remainder by 11, and the product will be
the Epact ; if the product exceed 30, divide it by 30, and
the remainder will be the Epact. When the Golden
Number is 1, the Epact is 29.

Example. What is the Epact for the year 184-6 ?

The Golden Number for 1846 is 4, hence (4—1 x 11
-^- 30) = 1 with a remainder of 3, which last is the Epact
for 1846.

The Epact for 1845 will be 22, the Golden Number
being 3.

* The Roman Indiction is of no use whatever in the Calendar. It
was a period of 1 5 years, in which the Romans collected a tax from
the countries which they had conquered. To find the Roman Indic-
tion add 3 to the year of Christ, and divide the sum by 15, the
remainder is the Indiction. Thus, the Indiction for 1845 is 3, for
(1845 +3) -f- 15 leaves a remainder of 3.

The Julian Period is of no use in the calendar ; however, it may be
found by adding 4713 to the year of Christ. Thus for the year 1844
we have 1844 + 4713 = 6557, the year of the Julian period.

i 6

180

OF THE CALENDAR.

Part II.

A TABLE of the Epacts till the Year 1900.

Epacts.

Golden
Numbers.

Epacts.

Golden
Numbers.

Epacts.

1
2
3
4
5

XXIX.
XI.
XXII.

III.

XIV.

7
8
9
10

XXV.
VI.
XVII.
XXVIII.
IX.

12
13
14
15

XX.

XII.
XXIII.
IV.

16
17
18
19

XV.
XXVI.
VII.
XVIIL

III. The Cycle of the Sun is a period of 28 years, after
which the days of the month return to the same days of
the week. This cycle has no reference to the apparent
motion of the sun, its chief use being to find the Domini-
cal Letters.

In order to connect the days of the week with the days
of the year, the first seven letters of the alphabet are
chosen to mark the several days of the week. These
letters are arranged in such a manner for every year, that
the letter A stands for the first of January, B for the
second, c for the third, and so on. The seven letters
being constantly repeated in their order through all the
days of the year, it is plain that the same letter will
answer to Sunday throughout the whole year, which is
therefore called the Sunday Letter.

To find the Cycle of the Sun for any Year till 1 900, and
likewise the Sunday Letter.

RULE. Add 9 to the given year, and divide the sum by
28, the remainder is the year of the solar cycle ; if there
be no remainder the solar cycle is 28. Then, in the fol-
lowing Table, against the solar cycle you will find the
Dominical Letter.

OR, To the given year add its fourth part, and increase
the sum by 6, divide the result by 7, and the remainder
taken from 7 leaves the number of the letter ; reckoning
A to be 1, B 2, c 3, D 4, E 5, F 6, and G 7. In a leap-
year this rule always gives the letter answering to the
months after February.

Chap. VII.

OF THE CALENDAR.

181

1 ED II 5 GF

9BA

13 DC

17 FE II 21 AGll 25 CB

2 C 6 E

10 G

14- B

18 D 22 F 26 A

3 B 7 D

11 F

15 A

19 c 23 E 27 G

4 A 1 8 c

12 E

16 G

20 B I) 24 D || 28 B

In a leap-year there are two Sunday Letters ; the left-
hand letter is used till the end of February, and the other
till the end of the year.

Example. What is the Dominical Letter for 1845?
(1845 + 9) -4- 28 leaves a remainder of 6; hence by the
above table E is the Sunday Letter.

Or, 1845 + 1^. + 6 = 2312, this divided by 7 leaves
2 remainder, which taken from 7 leaves 5, which, reckoning
by the second rule for finding the Sunday Letter in the
foregoing page, gives E as before.

The Dominical Letters for 1844 are GF.

IV. The Number of Direction is a number to be added
to the 21st of March to show on what day of the month
Easter Sunday falls. The earliest Easter possible is the
22d of March, the latest the 25th of April. Within these
limits are 35 days and the number of direction varies from
1 to 35. Thus, if Easter Sunday falls on the 22d of March
the number of direction is 1, if on the 23d it is 2; and so
on to the 31st, when the number of direction is 10. If
Easter Sunday falls on the first of April, the number of
direction is 11, if on the second it is 12, and so on to the
£5th of April, when the number of direction is 35.

A TABLE showing the number of Direction for finding Easter
Sunday by the Golden Number and Dominical Letter,

G. N.

"i7

1011

nlis
i

Domini. Letters.

B
C
.D
E
F
G

27
28
29
30
24
25

19
13
14

1.3
16
17

526
6J27
721
822
223
3!24
4'25

12
13
14
15
16
10
11

33'l9
3420
3521
2922
3023
3124
3218

'?
8

9
10
11

26
27
28
29
30
31
32

20: 6

21 7
15j 8
16i 9
1710
18' 4

26
27
28
29
23
24
25

12
IS

14
15
16
17

5
6

2
3
4

26
20
21
22
23
24
25

12
13
14
15

q
10

3319
3420
2821
2922
30:23
31J17
3218

12
6
7
8
9

lli

Example. On what day of the month and in what
month does Easter Sunday fall in the year 1845 ?

182

OF THE CALENDAR.

Part II.

The Golden Number already found is 3, and the Sunday
Letter E. Under 3, and in a line with E in the preceding
Table, you will find 2, which is the number of direction,
Easter Sunday falls therefore on the 23d of March ; for
March 21 + 2 = 23.

To find the PASCHAL FULL MOON, and thence Easter Day
by the Epact.

Add 6 to the Epact (if this sum exceeds 30, thirty
must be taken from it), and subtract the sum from 50, the
remainder is the Paschal full moon, or Easter limit. Add
4 to the number of the Dominical letter, subtract the sum
from the limit, and the remainder from the next higher
number, which will divide even by 7. The last remainder
added to the limit will give the number of days from the
first of March to Easter Day, both inclusive.

Example. Find the Paschal full moon and Easter Day
for the year 1845.

The Epact already given is 22, then 50 — (22 + 6) = 22,
Easter limit or Paschal full moon. The Dominical letter
is E, hence the number of the letter is 5 and 22 — (5 + 4)
= 13, the next higher number to which divisible by 7
without a remainder is 14. Therefore, 14 — 13 = 1, then
1 being added to 22, the limit gives 23, the days from the
1st of March; hence Easter day is the 23d of March as
before.

A TABLE for finding Easter till the year 1900.

Epacts.

Paschal Full
Moons.

Epacts.

Paschal Full
Moons.

XXIX.
XL

13 April E.
2 April A.

IX.
XX.

4 April c
24 Mar. F.

XXII.

22 Mar. D.

12 April D.

III.
XIV.

10 April B.
30 Mar. E.

XII.
XXIII.

1 April G.
21 Mar.c.

XXV.

18 April c.

IV.

9 April A

VI.
XVII.

7 April F.
27 Mar. B.

XV.
XXVI.

29 Mar. D.
17 April B.

XXVIII.

15 April G.

VII.

6 April E.

XVIII.

26 Mar. A.

Chap. VII. OP THE CALENDAR. 183

THE USE OF THE TABLE. Find the Epact (by some of
the preceding methods), against which, in the Table, is the
day of the Paschal full moon, with its corresponding
weekly letter.

Example. On what day does Easter fall in the year
1846?

The Epact is 3, against which, in the Table, is the 10th
of April, the day of the Paschal full moon ; and this
happens on a Friday, as indicated by the letter B ; D
being the Sunday letter for the year ; hence Easter Day
falls on the 12th of April.

Having found Easter Sunday, all the movable feasts
which depend upon it are known.

Septuagesima Sunday is 9 weeks ~] ^

Sexagesima Sunday is 8 weeks 1 £

Shrove Sunday or Quinquagesima Sunday is 7 weeks «
Shrove Tuesday and Ash Wednesday follow Quinqua- i ^

gesima Sunday

Quadragesima Sunday is 6 weeks *&

Palm Sunday a week
Good*Friday two days

Low Sunday is 1 week

Rogation Sunday is 5 weeks

Ascension Day or Holy Thursday, the Thursday fol-
lowing Rogation

Wliit Sunday is 7 weeks

Trinity Sunday is 8 weeks
Then follow all the Sundays after Trinity in order.

The Sundays between Ash Wednesday and Easter are

called Sundays in Lent; and the Sundays between Easter

and Whit Sunday are called Sundays after Easter.

V. By Act of Parliament Easter Day is the first Sunday

after the full moon which happens upon, or next after,

the 21st of March; and if the full moon fall on a Sunday,

Easter Day is the Sunday after.*

* The Act of Parliament does not refer to the astronomical full
moon as determined by exact calculation, but to the full moon as deter-
mined by the established calendar. Thus, in the year 1818, the astro-
nomical full moon was on Sunday the 22d of March, but the calendar
full moon was on Saturday the 21st, consequently Easter was the Sun-
day following, viz. the 22d.

OF THE CALENDAR.

Part II.

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«««ot»ao mo ~

— <M CO -* 10 50

-« IM « TJ- ic 50 1» x y.

12g

>o «o t~ oo o o -H

Chap. VII.

OF THE CALENDAR.

185

The Use of the Table. — By the foregoing Table the
moon's age may be found, by inspection onlv from the
year 1800 to 1894, inclusive, in the following manner: —
Find the proposed day, under the given month, in the
first part of the Table, or that which contains the months
and days. Then, on the same horizontal line, and under
the given year in the second part of the Table, will be found
the moon's age as required : observe, also, that N in this
part of the Table stands for new, and F for full moon.

EXAMPLE. Required the moon's age on the 21st of
February, 1845. Even with the day of the month found
in the first part of the Table, and under the year 1845 in
the latter part, is found the letter F, which shows that the
moon is full on that day.

In like manner it will be found that upon the 17th of
March, 1845, the moon's age is ten days.

The epact for any given year within the limits of the
Table is found at the bottom of the column, immediately
under the ^iven year. Thus, the epact for 1845 is 22.

In the following Table the right-hand column annexed
to the moon's age is used in finding the time of high
water in the succeeding problems relating to that subject.

Moon's
Age.

High Water.

Moon's
Age.

High Water.

Moon's
Age.

High Water.

Days.

H. M.

Days.

H. M.

Days.

H. M.

0 0

9 17

15 56

0 36

10 9

16 51

1 11

10 53

18 0

1 46

11 33

19 18

2 21

12 8

20 31

3 1

12 4,5

21 31

3 44

13 19

22 21

4 37

13 54

23 3

5 40

14 30

23 42

6 58

15 '.*

29£

24 0

8 14

The year, according to our present mode of reckoning,
consists of 365 days, for three years together, and every
fourth year consists of 366 days, which is called a leap-year,
in which the month of February has 29 days. But the
centuries which will not divide even by 4, such as 1700,
1800, 1.900, are not leap-years.

186

lls

f
ifJii

o <r>^J S^SS

05" 00 O O iS tS OC -•

<N (N fr* Ot

ooo oto c

<poo «

o'S

oo-ooo

Eccentricities in
English MUeS.

21,015,053
65,588,343

20,598,130
64,516,673

V, » £

Mean Velocities
per Hour in
EnKlish Miles.

W I

Time of performing
a Uevolution rountt
the Sun.

«!!

Mean Distances from the
Sun in round Numbers of
English Miles.

Ill

»iisi

f-i ^-i Cl

i i i i

t ••iii

|s|i

Ig £ 3

>^u »

187

s s s *.

& .

a*-

KM
HK

1 8, »S

S a*

Q —

> c?

SCO
«S

S 3 s tr

j 3 b

B:^

Coo

is it i

Ills 1

188

PART III.

CONTAINING PROBLEMS PERFORMED BY THE
TERRESTRIAL AND CELESTIAL GLOBES.

CHAPTER I.
Problems performed by the Terrestrial Globe.

PREPARATORY PROBLEM.

To cut a card so as to coincide with the convex surface of
the globe and the graduations on the brazen meridian.

RULE.* With the semi-diameter of the globe for a
radius (that is, with a radius of six inches for a twelve-
inch globe, nine inches for an eighteen-inch globe, and so
on), and any point, c, as a centre, describe the arc A B
of any convenient length. From c, through the points
A and B, draw the lines CAD, c B E, and connect the

* This problem and figure was first given by me, in the new edition
of Goldsmith's Grammar of Geography. — En."

Chap. 1. THE TERRESTRIAL GLOBE. 189

points D and Ewith a plain or ornamental line: then if the
figure A B D E be cut smoothly out with any very sharp
tool, the arc A B will fit the convex surface, and the sides
A D, B E will become produced radii of the globe, corre-
sponding exactly with the divisions marked on the brazen
meridian. This card, for want of a better name, I have
called an INDEX CARD.

The use of this card is to read off the brazen meridian
correctly, as well as to preserve the globe from the in-
juries it frequently sustains from the pernicious custom of
applying the point of a pair of compasses, &c. to its surface,
particularly in working those problems that require a ro-
tation of the globe on its axis, at the same time that a
certain point of declination or latitude is preserved.*

PROBLEM I.

To find the latitude of any given place.
RULE. Bring the given place to that part of the brass
meridian which is numbered from the equator towards
the poles : the degree, or intermediate part of a degree,
directly above the place, is the latitude. If the place be
on the north side of the equator, the latitude is north : if
it be on the south side, the latitude is south. -j-

EXAMPLES. What is the latitude of Edinburgh ?

Answer. 56° north.

2. Required the latitudes of the following places :
Amsterdam Florence Philadelphia

Archangel Gibraltar Quebec

Barcelona Hamburgh Rio Janeiro.

* In applying the Index Card, place the flat side of the card against
the graduated side of the brazen meridian, while the concave edge
rests on the surface of the globe : then, if one of the extreme ends of
the concave arc be brought exactly to touch the given place, star, &c.,
the straight edge of the Index Card will cut the true latitude of the
place or declination of the star, &c., which will be read off as correctly
and easily as if the graduated edge of the meridian itself extended to
the very surface of the globe. Any degree, or even a quarter of a degree,
of the equator, ecliptic, &c. intersected by the brazen meridian, may
be read off with equal correctness and facility by a similar application
of the Index Card. — ED.

t Observe, that in using either globe, it is to be so placed, that the
graduated side of the brazen meridian may be towards the right hand.
-En.

190 PROBLEMS PERFORMED BY Part III.

3. Find all the places on the globe which have no lati-
tude.

4. What is the greatest latitude a place can have ?

PROBLEM II.

To find all those places which have the same latitude as
any given place.

RULE. Bring the given place to that part of the brass
meridian which is numbered from the equator towards
the poles, and observe its latitude ; turn the globe round,
and all places passing under the observed latitude are
those required.

All places in the same latitude have the same length of day and
night, and the same seasons of the year, though, from local circum-
stances, they may not have the same atmospherical temperature. See
the note, page 17.

EXAMPLES. 1. What places have the same, or nearly
the same, latitude as Madrid ?

Answer. Minorca, Naples, Constantinople, Samarcand, Philadel-
phia, Pekin, &c.

2. What inhabitants of the earth have the same length
of days as the inhabitants of Edinburgh ?

3. What places have nearly the same latitude as Lon-
don?

4. What inhabitants of the earth have the same seasons
of the year as those of Ispahan ?

5. Find all places of the earth which have the longest
day the same length as at Port Royal in Jamaica.

PROBLEM III.
To find the longitude of any place.

RULE. Bring the given place to the brass meridian,
the number of degrees and parts of a degree on the equator,
reckoning from the meridian passing through London to
the brass meridian, is the longitude. If the place lie to
the right hand of the meridian passing through London,
the longitude is east ; if to the left hand, the longitude is
west.

On Adams' and Cary's globes there are two rows of figures above
the equator. When the place lies to the right hand of the meridian of
London, the longitude must be counted on the upper line ; when it
lies to the left hand it must be counted on the lower line. Bardirts

THE TERRESTRIAL GLOBE. 191

New British Globes have also two rows of figures above the equator,
but the lower line is always used in reckoning the longitude.

EXAMPLES. 1. What is the longitude of Petersburg ?

Answer. 30%° east.

2. What is the longitude of Philadelphia ?
Ansiver. 75£° west.

3. Required the longitudes of the following places :
Aberdeen Bombay Carlscrona
Alexandria Botany Bay Cayenne
Barbadoes Canton Civita Vecchia.

4. What is the greatest longitude a place can have ?

PROBLEM IV.

To find all those places that have the same longitude as a
given place.

RULE. Bring the given place to the brass meridian,
then all places under the same edge of the meridian from
pole to pole have the same longitude.

All people situated under the same meridian, from 66° 28' north
latitude to 66° 28' south latitude, have noon at the same time ; or, if
it be one, two, three, or any number of hours before or after noon
with one particular place, it will be the same hour with every other
place situated under the same meridian.

EXAMPLES. 1. What places have the same, or nearly
the same, longitude as Stockholm ?

Answer. Dantzic, Presburg, Tarento, the Cape of Good Hope, &c.

2. What places have the same longitude as Alexandria ?

3. When it is ten o'clock in the evening at London,
what inhabitants of the earth have the same hour?

4. What inhabitants of the earth have midnight when
the inhabitants of Jamaica have midnight ?

5. What places of the earth have the same longitude as
the following places ?

London Quebec The Sandwich Islands

Pekin Dublin Pelew Islands.

PROBLEM V.
To find the latitude and longitude of anyplace.

RULE. Bring the given place to that part of the brass
meridian which is numbered from the equator towards the

192

PROBLEMS PERFORMED BY

Part III.

poles ; the degree or intermediate part of a degree imme-
diately above the place is the latitude, and the degree on
the equator, cut by the brass meridian, is the longitude.

This problem is only an exercise of the first and third.

EXAMPLES. 1. What are the latitude and longitude of
Petersburgh ?

Answer. Latitude CO0 N. ; longitude S0|° E.
2. Required the latitudes and longitudes of the follow-
ing places :

Cusco Lima

Copenhagen Lizard

Durazzo Lubec

Elsinore Malacca

Flushing Manilla

Acapulco

Aleppo

Algiers

Archangel

Belfast

Bergen

Cape Guardafui Medina.

PROBLEM VI.

To find any place on the globe having the latitude and
longitude of that place given.

RULE. Find the given longitude on the equator, and
bring it to that part of the brass meridian marked 0, then
under the given latitude, on the brass meridian will be
found the place required.

EXAMPLES. 1. What place has 151^° east longitude
and 34° south latitude ?

Answer. Botany Bay.

2. What places have nearly the following latitudes and
longitudes ?

Latitudes.
50° N.

48£N.
56 N.
52i N.
31 N.

3|S.
34iS.
82* N.

Longitudes.

Latitudes.

6° W.

19§° N.

16| E.

60 N.

3J W.

* s.

4f E.

47 N.

30 E.

59£ N.

39 E.

8i N.

18£E.

5 S.

102J E.

23 S.

58£ W.

36 N.

52f E.

32i N.

Longitudes.
100° W.

30|E.

78 W.

70 W.

18 E.

81£ E.
119f E.

42f W.
5£W.

17 W.

Chap. 1. THE TERRESTRIAL GLOBE. 193

PROBLEM VII.

To find the difference of latitude between any two places.

RULE. Find the latitudes of both the places (by ProbJ.);
then, if the latitudes be both north or both south, sub-
tract the less latitude from the greater, and the remainder
will be the difference of latitude ; but, if the latitudes be
one north and the other south, add them together, and
their sum will be the difference of latitude.

EXAMPLES. 1. What is the difference of latitude be-
tween Philadelphia and Petersburg ?

Answer. 20 degrees.

2. What is the difference of latitude between Madrid
and Buenos Ayres ?

Answer. 75 degrees.

3. Required the difference of latitude between the fol-
lowing places :

London and Rome
Delhi and Cape Comorin
Vera Cruz and Cape Horn
Mexico and Botany Bay
Astracan and Bombay
St. Helena and Manilla
Copenhagen and Toulon
Brest and Inverness
Cadiz and Sierra Leone

Alexandria and the Cape

of Good Hope
Pekin and Lima
St, Salvador and Surinam
Washington and Quebec
Porto Bello and the Straits

of Magellan

Trinidad I . and Trincomai£
Bencoolen-and Calcutta.

4. What two places on the globe have the greatest
difference of latitude ?

PROBLEM VIII.
To find the difference of longitude between any two places.

RULE. Bring one of the given places to the brass me-
ridian, and mark its longitude on the equator ; then bring
the other place to the brass meridian, and the number ot
degrees between its longitude and the above mark,
counted on the equator, the nearest way round the globe,
will show the difference of longitude.

OR, Find the longitudes of both the places (by Prob.
III.); then, if the longitudes be both east or both west, sut>

194? PROBLEMS PERFORMED BY Part HI.

tract the less longitude from the greater, and the remainder
will be the difference of longitude : but, if the longitude
be one east and the other west, add them together, and
their sum will be the difference of longitude, if it does not
exceed 180 degrees.

When this sum exceeds 180 degrees, take it from 360,
and the remainder will be the difference of longitude.

EXAMPLES. 1. What is the difference of longitude be-
tween Barbadoes and Cape Verd ?

Answer. 43|°.

2. What is the difference of longitude between Buenos
Ayres and the Cape of Good Hope ?

Answer. 77°.

3. What is the difference of longitude between Botany
Bay and O'why'hee ?

Answer. 52|°.

4. Required the difference of longitude between the
following places : —

Vera Cruz and Canton

Bergen and Bombay

Columbo and Mexico

Juan Fernandez I. and Ma-
nilla

Pelew I. and Ispahan

Boston in Amer. and Berlin

5. What is the greatest difference of longitude com-
prehended between two places ?

Constantinople and Batavia
Bermudas I. and I. of Rhodes
Portpatrick and Berne
Mount Hecla and Mount

Vesuvius

Mount jiEtna and Teneriffe
North Cape and Gibraltar.

PROBLEM IX.
To find the nearest distance between any two places.

RULE. The shortest distance between any two places
on the earth, is an arc of a great circle contained between
the two places. Therefore, lay the graduated edge of the
quadrant of altitude over the two places, so that the di-
vision marked 0 may be on one of the places, the degrees
on the quadrant comprehended between the two places
will give their distance ; and if these degrees be multi-
plied by 60, the product will give the distance in geo-

Chap. 1. THE TERRESTRIAL GLOBE. 195

graphical miles ; or, multiply the degrees by 69*1, and the
product will give the distance in English miles.

OR, Take the distance between the two places with a
pair of compasses, and apply that distance to the equator,
which will show how many degrees it contains.

If the distance between the two places should exceed
the length of the quadrant, stretch a piece of thread over
the two places, and mark their distance ; the extent of
thread between these marks, applied to the equator, from
the meridian of London, will show the number of degrees
between the two places.

EXAMPLES. 1. What is the nearest distance between
the Lizard and the Island of Bermudas ?

45f distance in degrees.

2700
30
15

745 geographical miles.

45 '75 distance in degrees.

69-1,

4575
41175
27450

3161 -325 English miles.

2. What is the direct distance between London and
Jamaica, in geographical and English miles ?

3. What is the extent of Europe, in English miles,
from Cape Matapan in the Morea, to the North Cape in
Lapland ?

4*. What is the extent of Africa from Cape Verd to
Cape Guardafui ?

5. What is the extent of South America, from Cape
Blanco in the west to Cape St. Roque in the east ?

6. Suppose the track of a ship to Madras be from the
Lizard to St. Anthony, one of the Cape Verd Islands,
thence to St. Helena, thence to the Cape of Good Hope,
thence to the east of the Mauritius, thence a little to the
south-east of Ceylon, and thence to Madras ; how many
English miles is the Land's End from Madras ?

The following table is calculated thus : — Radius is to the length of a
degree upon the equator, as the co-sine of the given latitude is to the
length of a degree in that latitude. See this proposition illustrated in
Keittts Trigonometry, page 296. fourth edition.
K 2

196

PROBLEMS PERFORMED BY

Part III.

Deg.

Lat.

Geog.
Miles.

English
Miles.

Deg.
Lat.

Geog.
Miles.

English
Miles.

Deg.

Lat.

Geog.

Miles.

English
Miles.

60-00

69-07

51-43

59'13

29-09

33-45

59-99

69-06

50-88

58-51

28-17

32-40 1

59-96

69-03

50*32

57-87

27-24

31-33

59-92

68-97

49'74

57-20

26-30

30-24

59-85

68-90

49-15

56-51

25-36

29-15

59*77

68-81

48-54

55-81

24-40

28-06

59-67

68-62

47-92

55-10

23-45

26-96

59-55

68-48

47-28

54-37

22-48

25-85

59-42

68-31

46-63

53-62

21-50

24-73

59-26

68-15

45-96

52-85

20-52

23-60

59-09

67-95

45-28

52-07

19-53

22-47

58-89

67-73

44-59

51-27

18-54

21-32

58-69

67-48

43-88

50-46

17-54

20-17

58-46

67-21

43-16

49-C3

16-54

19-02

58-22

66-95

42-43

48-78

15-53

17-86

57-95

66-65

41-68

47-93

14-52

16-70

57-67

66-31

40-92

47-06

13-50

]5-52

57-38

65-98

40-15

46-16

12-48

14-35

57-06

65-62

39-36

45- 6 | 79

11-45

13-17

56-73

65-24

38-5^

44'35 80

10-42

11-98

56-38

64-84

37-76

43-42

9-38

10-79

56-01

64-42

36-94

42-48

8-35

9-59

55-63

63-97

36-11

41-53

7-31

8-41

55-23

63-51

35-27

40-56

6-27

7-21

54-81

63-03

34-41

39-58

5-22

6-00

54-38

62-53

33-53

38-58

4-18

4-81

53-93

62-02

32-68

37-58

3-14

3-61

53-46

61-48

3J-79

36-57

2-09

241

52-97

60-93

30-90

35-54

1-05

1-21

52-48

60-35

30-00

34-50

0-00

51-96

59-75

Length of a degree 69 '07 English miles.

PROBLEM X.

A place being given on the globe, to find all places, which
are situated at the same distance from it as any other
given place.

RULE. Lay the graduated edge of the quadrant of
altitude over tiie two places, so that the division marked
o may be on one of the places, then observe what degree
of the quadrant stands over the other place ; move the
quadrant entirely round, keeping the division marked o

Chap. I. THE TERRESTRIAL GLOBE. IQy

in its first situation, and all places over which the observed
degree passes will be those sought.

OR, Place one foot of a pair of compasses in one of the
given places, and extend the other foot to the other given
place ; a circle described from the first place as a centre,
with this extent, will pass through all the places sought.

If the distance between the two given places should exceed the
length of the quadrant, or the extent of a pair of compasses, stretch a
piece of thread over the two places, as in the preceding problem.

EXAMPLES. 1. It is required to find all the places on
the globe which are situated at the same distance from
London as Warsaw is ?

Answer. Konigsburg, Buda, Posega, Alicant, &c.

2. What places are nearly at the same distance from
London as Petersburg is ?

3. What places are nearly at the same distance from
London as Constantinople is ?

4. What places are nearly at the same distance from
Rome as Madrid is ?

PROBLEM XI.

Given the latitude of a place and its distance from a given
place, to find that place whereof the latitude is given.

RULE. If the distance be given in English or geogra-
phical miles, turn them into degrees by dividing by 69-1
for English miles, or 60 for geographical miles ; then put
that part of the graduated edge of the quadrant of alti-
tude which is marked 0 upon the given place, and move
the other end eastward or westward (according as the re-
quired place lies to the east or west of the given place),
till the degrees of distance cut the given parallel of lati-
tude : under the point of intersection you will find the
place sought.

OR, Having reduced the miles into degrees, take the
same number of degrees from the equator with a pair of
compasses, and with one foot of the compasses in the
given place, as a centre, and this extent of degrees, de-
scribe a circle on the globe ; turn the globe till some
K 3

198 PROBLEMS PERFORMED BY Part III.

point of this circle falls under the given latitude on the
brass meridian, and the place which coincides with this
point of the circle is the place required.

EXAMPLES. 1. A place in latitude 60° N. is 1312-9
English miles from London, and it is situated in E. longi-
tude ; required the place ?

Answer. Divide 1312-9 by 69'1 miles, the quotient will give 19
degrees ; hence the required place is Petersburg.

2. A place in latitude 32^° N. is 1350 geographical
miles from London, and it is situated in w. longitude ;
required the place ?

Answer. Divide 1350 by 60, the quotient is 22° SO/, or 22f de-
grees ; hence the required place is the west point of the island of
Madeira.

3. What place, in E. longitude and 41° N. latitude, is
1520-2 English miles from London?

4. What place in w. longitude and 13° N. latitude, is
3660 geographical miles from London ?

PROBLEM XII.

Given the longitude of a place and its distance from a given
place} to find that place whereof the longitude is given.

RULE. If the distance be given in English or geogra-
phical miles, turn them into degrees by dividing by 69-1
for English miles, or 60 for geographical miles ; then put
that part of the graduated edge of the quadrant of altitude
which is marked 0 upon the given place, and move the
other end northward or southward (according as the re-
quired place lies to the north or south of the given place),
till the degrees of distance cut the given longitude : under
the point of intersection you will find the place sought.

OR, Having reduced the miles into degrees, take the
same number of degrees from the equator with a pair of
compasses, and with one foot of the compasses in the
given place, as a centre, and this extent of degrees, describe
a circle on the globe ; bring the given longitude to the
brass meridian, and you will find the place, upon the circle,
under the brass meridian.

Chap.L THE TERRESTRIAL GLOBE. 199

EXAMPLES. 1. A place in north latitude, and in 60
degrees west longitude, is 4?215*1 English miles from Lon-
don ; required the place ?

Answer. Divide 4215'! miles by 69'1 miles, the quotient will
give 61 degrees; hence the required place is the island of Barba-
does.

2. A place in north latitude, and in 75£ degrees west
longitude, is 3120 geographical miles from London ; what
place is it?

3. A place in 31|degrees east longitude, and situated
southward of London, is 2211*2 English miles from it ; re-
quired the place ?

4. A place in 29 degrees east longitude, and situated
southward of London, is 1520*2 English miles from it; re-
quired the place ?

PROBLEM XIII.

To find how many miles make a degree of longitude in any
given parallel of latitude.

RULE. Lay the quadrant of altitude parallel to the
equator, between any two meridians in the given latitude,
which differ in longitude 15 degrees * ; the number of de-
grees intercepted between them, multiplied by 4, will give
the length of a degree in geographical miles. The geo-
graphical miles may be brought into English miles by
multiplying by 69-1 and dividing by 60.

OR, Take the distance between two meridians, which
differ in longitude 1 5 degrees in the given parallel of lati-
tude, with a pair of compasses ; apply this distance to the
equator, and observe how many degrees it makes : with
which proceed as above.

Since the quadrant of altitude will measure no arc truly but that of
a great circle ; and a pair of compasses will only measure the chord of an
arc, not the arc itself ; it follows that the preceding rule cannot be
mathematically true, though sufficiently correct for practical purposes.

* The meridians on CART'S large globes are drawn through every
ten degrees. The rule will answer for these globes by reading 10 de-
grees for 15 degrees, and multiplying by 6 instead of 4.
K 4,

200 PROBLEMS PERFORMED BY Part 111

When great exactness is required, recourse must be had to calculation.
See the table in the note to Problem IX. page 195.

The above rule is founded on a supposition that the number of de-
grees contained between any two meridians, reckoned on the equator,
is to the number of degrees contained between the same meridians,
on any parallel of latitude, as the number of geographical miles con-
tained in one degree of the equator, is to the number of geographical
miles contained in one degree on the given parallel of latitude. Thus,
in the latitude of London, two places which differ 15 degrees in lon-
gitude are 9f degrees distant by the rule. Hence,
15° : 9£°: : 60m. : 37m., or 15° r 60m. : : 9|° : 37m., but 15 is to
SO as 1 is to 4, therefore, 1:4:: 9£ : 37 geographical miles con-
tained in one degree. Now, any nunber of geographical miles (as
before observed) may be brought into English miles by multiplying
by 69-1 and dividing by 60.

EXAMPLES. 1. How many geographical and English
miles make a degree in the latitude of Pekin ?

Answer. The latitude of Pekin is 40° north : the distance between
two meridians in that latitude (which differ in longitude 15 degrees) is
H;L degrees. Now 11^ degrees multiplied by 4, produces 46 geo-
graphical miles for the length of a degree of longitude in the latitude
of Pekin ; and if 46 be multiplied by 69-1 and the product divided by
60, it will give 52-97* or nearly 53 for the length of a degree in En-
glish miles. OR, by the rule of three, 15°: 69-lm. : : 11£°: 52 -97 miles.

2. How many miles make a degree in the parallels of
latitude wherein the following places are situated ?
Surinam Washington Spitzbergen

Barbadoes Quebec Cape Verd

Havannah Skalholt Alexandria

Bermudas I. North Cape Paris.

PROBLEM XIV
To find the bearing of one place from anot/ier.

RULE. If both the places be situated on the same pa-
rallel of latitude, their bearing is either east or west from
each other ; if they be situated on the same meridian,
they bear north and south from each other ; if they be
situated on the same rhumb-line *, that rhumb-line is

* On ADAMS' globes there are two compasses drawn on the equa-
tor, each point of which may be called a rhumb-line, being drawn so
as to cut all the meridians in equal angles. One compass is drawn on

Chap. I. THE TERRESTRIAL GLOBE. 201

their bearing : if they be not situated on the same rhumb-
line, lay the quadrant of altitude over the two places, and
that rhumb-line which is the nearest of being parallel to
the quadrant will be their bearing.

OR, If the globe have no rhumb-lines drawn on it, make
a small mariner's compass (such as in Platel. Fig.4>.)
and apply the centre of it to any given place, so that the
north and south points may coincide with some meridian ;
the other points will shew the bearings of all the circum-
jacent places, to the distance of upwards of a thousand
miles, if the centrical place be not far distant from the
equator.

EXAMPLES. 1. Which way must a ship steer from the
Lizard to the island of Bermudas ?

Answer. W.S.W.

2. Which way must a ship steer from the Lizard to the
island of Madeira ?

Answer. S.S.W.

3. Required the bearing between London and the fol-
lowing places ?

Amsterdam Copenhagen Petersburg

Athens Dublin Prague

Bergen Edinburgh Rome

Berlin Lisbon Stockholm

Berne Madrid Vienna

Brussels Naples Warsaw.

Buda Paris

PROBLEM XV.
To find the angle of position between two places.

RULE. Elevpte the north or south pole, according as
the latitude is north or south, so many degrees above the
horizon as are equal to the latitude of one of the given
places ; bring that place to the brass meridian, and screw
the quadrant of altitude upon the degree over it ; next

a vacant place in the Pacific ocean, between America and New Hol-
land ; and another, in a similar manner, in the Atlantic between
Africa and South America. There are no rhumb-lines on GARY'S,
BARDIN'S, or ADDISON'S globes.

K 5

202 PROBLEMS PERFORMED BY Part 111.

move the quadrant till its graduated edge falls upon the
other place ; then the number of degrees on the wooden
horizon, between the graduated edge of the quadrant and
the brass meridian, reckoning towards the elevated pole,
is the angle of position between the two places.

EXAMPLES. 1. What is the angle of position between
London and Prague ?

Answer. 90 degrees from the north towards the east : the quadrant
of altitude will fall upon the east point of the horizon, and pass over
or near the following places, viz. Rotterdam, Frankfort, Cracow,
Ockzakov, Caffa, south part of the Caspian Sea, Guzerat in India,
Madras, and part of the island of Ceylon. Hence all these places,
have the same angle of position from London.

2.1 What is the angle of position between London and
Port Royal in Jamaica ?

Answer. 90 degrees from the north towards the west ; the quadrant
of altitude will fall upon the west point of the horizon.

3. What is the angle of position between Philadelphia
and Madrid ?

Answer. 65 degrees from the north towards the east ; the quadrant
of altitude will fall between the E.N.E. and N.E. by E. points of the
horizon.

4. Required the angles of position between London
and the following places ?

Amsterdam Copenhagen Rome

Berlin Cairo Stockholm

Berne Lisbon Petersburg

Constantinople Madras Quebec.

The preceding problem has been the occasion of many disputes
among writers on the globes. Some suppose the angle of position to
represent the true bearing of two places, viz. that point of the compass
upon which any person must constantly sail or travel, from the one place
to the other ; while others contend that the angle of position between two
places is very different from their bearing by the mariner's compass.
We shall here endeavour to set the matter in a clear point of view.
The following figure represents a quarter of the sphere, stereographi-
cally projected on the plane of the meridian with the half meridians and
parallels of latitude drawn through every ten degrees ; p represents the
north pole, and E Q a portion of the equator. Now, by attending to
the manner of finding the angle of position, as laid down in the fore-
going problem, we shall find that the quadrant of altitude always forms
the base of a spherical triangle, the two sides of which triangle are tlie
complements of the latitudes of the two places, and the vertical angle is
their difference of longitude. The angles at the base of this triangle are
the angles of position between the two places.

Chap. I. THE TERRESTRIAL GLOBE. 203

1 . Wlien the two places are situated on the same parallel of latitude.

Let two places L and o be situated
in latitude 50° north, and differ-
ing in longitude 48° 50', which will
nearly correspond with the Land's
End and the eastern coast of New-
foundland (see the note to Prob. IX) ;
then or and LP will be each 40 de-
grees, the angle OPL, measured by
the arc w Q, will be 48° 507 ; whence
the arc of nearest distance o n L
may be found (by case III. page
245, Keith's Trigonometry) being 3O°j
39' 6", the angle PLO equal to POL,
the triangle being isosceles, is 70°
49' 30" ; and if n be the middle point between L and o, the latitude
of that point will be found to be 52° 37' north, and the angles
p ?i L and P n o will be right angles. Now, if an indefinite number
of points be taken along the edge of the quadrant of altitude, viz. on
the arc L w o, the angle of position between L and each of these points
will be N. 70° 49' 30" W. ; but, if it were possible for a ship to sail
along the arc L n o, by the compass, her latitude would gradually in-
crease between L and n, from 50° N. to 52° 37' N. ; and the courses
she must steer would vary from 70° 49' 30" at L, to 90° at n. In
sailing from n to o, she must decrease her latitude from 52° 37' N. to
50° N. and her courses must vary from 90°, or directly west, to
70° 49' 30" ; but, if a ship were to sail along the parallel of latitude
L m o, her course would be invariably due west. Hence it follows
that, if two places be situated on the same parallel of latitude, the an-
gle of position between them cannot represent their true bearing by the
mariner's compass.

COROLLARY. If the two places were situated on the equator as at
w and Q, the angle of position between Q and w and between Q and
all the intermediate points, as at N, would be 90 degrees. In this
case therefore, and in this only, the angle of position shews the true
bearing by the compass.

2. If the two places differ both in latitudes and longitudes. '•• . ,

Let L represent a place in latitude 50° N. ; B a place in latitude
13° SO' N., and let their difference of longitude BPL, measured by the
arc b Q, be 52° 58'. The angle of position between L and B (calcu-
lated by spherical trigonometry) will be found to be S. 68° 57' W.
and the angle of position between B and L will be N. 38° 5' E.,
whereas, the direct course by the compass from L to B (calculated by
Mercators Sailing) is S. 50° 6' W., and from B to L it is N. 50° 6' E.
If we assume any number of points on the arc L B, the angle of posi-
tion between L and each of these points will be invariable ; viz. p L v,
p L t} P L y, p i, s, p L r, &c. are each equal to 68° 57' : while the
K 6

204 PROBLEMS PERFORMED BY Part III

angle of position between each of these places and t, viz. P v L, p t L,
v y L, P s t, P r L, &c. is continually diminishing. If a ship, there-
fore, were to sail from L, on a S. 68° 51' W. course by the mariner's
compass, she would never arrive at B ; and were she to sail from B,
on a N. 38° 5' E. course by the compass, she would never arrive
at L.

Hence an angle of position between two places cannot represent their
bearing, except those places be on the equator, or upon the same me-
ridian.

PROBLEM XVI.

To find tfie Antceci, Periceci, and Antipodes to tlie
in/iabitants of any place.

RULE. Place the two poles of the globe in the horizon,
and bring the given place to the eastern part of the hori-
zon ; then if the given place be in north latitude, ob-
serve how many degrees it is to the northward of the east
point of the horizon ; the same number of degrees to the
southward of the east point will shew the Antceci; an
equal number of degrees, counted from the west point
of the horizon towards the north, will shew the Perioeci ;
and the same number of degrees, counted towards the
south of the west, will point out the Antipodes. If the
place be in south latitude, the same rule will serve by
reading south for north, and the contrary.

OR THUS :

For the Antceci. 'Bring the given place to the brass
meridian and observe its latitude, then in the opposite
hemisphere, under the same degree of latitude, you will
find the Antceci.

For the Periceci. Bring the given place to the brass
meridian, and set the index of the hour circle to 12, turn
the globe half round, or till the index points to the other
12, then under the latitude of the given place you will
find the Perioeci.

Hpr the Antipodes. * Bring the given place to the brass
meridian, and set the index of the hour circle to 12, turn
the globe half round, or till the index points to the other

THE TERRESTRIAL GLOBE. 20,5

12, then under tlie same degree of latitude with the given
place, but in the opposite hemisphere;, you will find the
Antipodes.

EXAMPLES. 1. Required the Antceci, Perioeci, and
Antipodes, to the inhabitants of the island of Bermudas ?

Answer. Their Antoeci are situated in Paraguay, a little N.W. of
Buenos Ayres; their Perioeci in China, N.W, of Nankin; and their
Antipodes in the S. W. part of New Holland.

2. Required the Antceci, Perioeci, and Antipodes, to
the inhabitants of the Cape of Good Hope ?

3. Captain Cook, in one of his voyages, was in 50 de-
grees .south latitude and 180 degrees of longitude ; in
what part of Europe were his Antipodes ?

4. Required the Antceci to the inhabitants of the Falk-
land islands ?

5. Required the Periceci to the inhabitants of the Phi-
lippine islands ?

6. What inhabitants of the earth are Antipodes to
those of Buenos Ayres ?

PROBLEM XVII.

To find at what rate per hour the inhabitants of any given
place are carried, from west to east, by the revolution of
the earth on its axis.

RULE. Find how many miles make a degree of longi-
tude in the latitude of the given place (by Problem XIII.)
which multiply by 15 for the answer.*

OR, Look for the latitude of the given place in the
table, Problem IX., against which you will find the num-
ber of miles contained in one degree ; multiply these miles

* The reason of this rule is obvious, for if m be the number of
miles contained in a degree, we have 24 hours : 360° x m : : 1 hour
: the answer; but, 24 is contained 15 times in 360 ; therefore 1 hour
: 15 x m. : : 1 hour : the answer ; that is, on a supposition that the-
earth turns on its axis from west to east in 24 hours ; but we have
before observed that it turns on its axis in 23 hours 56 min. 4 sec.
which will make a small difference not worth notice.

206 PROBLEMS PERFORMED BY Part III.

by 15, and reject two figures from the right hand of the
product ; the result will be the answer.

EXAMPLES. 1. At what rate per hour are the inhabit-
ants of Madrid carried from west to east by the revolu-
tion of the earth on its axis ?

Answer. The latitude of Madrid is about 40° N. 'where a degree of
longitude measures 46 geographical, or 53 English miles (see Ex-
ample 1. Prob. XIII.) Now 46 multiplied by 15 produces 690 ; and
53 multiplied by 15 produces 795; hence the inhabitants of Madrid
are carried 690 geographical, or 795 English miles per hour.

By the Table. Against the latitude 40 you will find 45-96 geogra-
phical miles, and 52-85 English miles : Hence,

45-96 x 15 = 689-40 and 52-85 x 15=792-75: by rejecting the two
right-hand figures from each product, the result will be 689 geogra-
phical miles, and 792 English miles, agreeing nearly with the above.

2. At what rate per hour are the inhabitants of the fol-
lowing places carried from west to east by the revolution
of the earth on its axis ?

Skalholt Philadelphia Cape of Good Hope

Spitzbergen Cairo Calcutta

Petersburg Barbadoes Delhi

London Quito Batavia.

PROBLEM XVIII.

A particular place, and the hour of the day at that place,
being given, to find what hour it is at any other place.
RULE. Bring the place at which the time is given to
the brass meridian, and set the index of the hour circle
to the given hour; turn the globe till the other place
comes to the meridian, and the index will show the re-
quired tfme.

OR, WITHOUT THE HOUR-CIRCLE.

Find the difference of longitude between the two places
(by Problem VIII.) and turn it into time by allowing 15
degrees to an hour, or four minutes of time to one degree.
The difference of longitude in time will be the difference
of time between the two places, with which proceed as
above. Degrees of longitude may be turned into time by
multiplying by 4 ; observing that minutes or miles of lon-
gitude, when jnultiplied by 4-, produce seconds of time ;
and degrees of longitude, when multiplied by 4, produce
minutes of time.

Chap. I. THE TERRESTRIAL GLOBE. 207

If the globe have two rows of figures on the hour circle, that row
must be used which is numbered from west to east j this is generally
the outermost row.

EXAMPLES, 1. When it is ten o'clock in the morning
at London, what hour is it at Petersburg ?

Answer. Twelve o'clock at noon.

OR, The difference of longitude between Petersburg and London is
30° 25', which multiplied by 4 produces two hours 1 min. 40 sec. the
difference of time shewn by the clocks of London and Petersburg :
hence as Petersburg lies to the east of London ; when it is ten o'clock
in the morning at London, it is one minute and forty seconds past
twelve at Petersburg.

2. When it is two o'clock in the afternoon at Alexandria
in Egypt, what hour is it at Philadelphia ?

Answer. Seven o'clock in the morning.

Or, The longitude of Alexandria is 30° 16' E.

The longitude of Philadelphia is 75 19 W.

Difference of longitude 105 35

Difference of longitude in time 7 h. 2m. 20 sec.,

!the clocks at Philadelphia are slower than those of Alexandria : hence
when it is two o'clock in the afternoon at Alexandria, it is 57 m. 40 sec.
past six in the morning at Philadelphia.

3. When it is noon at London, what hour is it at Cal-
cutta?

4. When it is ten o'clock in the morning at London,
what hour is it at Washington ?

5. When it is nine o'clock in the morning at Jamaica,
what o'clock is it at Madras ?

6. My watch was well regulated at London, and when
I arrived at Madras, which was after a five months' voyage,
it was four hours and fifty minutes slower than the clocks
there. Had it gained or lost during the voyage? and
how much ?

PROBLEM XIX.

A particular place and the hour of the day being given, to
find all places on the globe where it is then noont or any

RULE. Bring the given place to the brass meridian,
and set the index to the given hour ; turn the globe till

208 PROBLEMS PERFORMED BY Part III.

the index points to 12 at noon or to the hour proposed,
then the places required will be found under the brass

meridian.

OR, WITHOUT THE HOUR-CIRCLE.

Reduce the difference of time between the given place
and the required places into minutes; these minutes,
divided by 4, will give degrees of longitude ; if there be
a remainder after dividing by 4, multiply it by 60, and
divide the product by four, the quotient will be minutes
or miles of longitude. The difference of longitude between
the given place and the required places being thus deter-
mined, if the hour at the required places be earlier than
the hour at the given place, the required places lie so
many degrees to the westward of the given place as are
equal to the difference of longitude; if the hour at the
required places be later than the hour at the given place,
the required places lie so many degrees to the eastward of
the given place as are equal to the difference of longitude.
EXAMPLES. 1. When it is noon at London, at what
places is it half-past eight o'clock in the morning ?

Answer. The eastern coast of Newfoundland, Cayenne, part of
Paraguay, &c.

OR, The difference of time between London, the given place, and
the required places, is 3 hours 3O min.

3 h. 30 m. The difference of longitude between the

60 given place and the required places is 52° 3O.

— , - The hour at the required places being earlier

4) 2 10m. than that at the given place, they lie 52° 30/

- westward of the given place. Hence, all

52° — 2' places situated in 52° SO' west longitude from

60 London, are the places sought, and will be

- found to be Cayenne, &c. as above.

4)120

2. When it is two o'clock in the afternoon at London,
at what places is it £ past five in the afternoon ?

Answer. The Caspian Sea, western part of Nova Zembla ; the
Island of Socotra, eastern part of Madagascar, &c.

3. When it is f past four in the afternooon at Paris,
where is it noon ?

Chap. I. THE TERRESTRIAL GLOBE. 2Q9

4-. When it is f past seven in the morning at Ispahan,
where is it noon ?

5. When it is noon at Madras, where is it J past six
j'clock in the morning ?

6. At sea in latitude 40° north, when it was ten o'clock
in the morning by the time-piece, which shews the hour
at London, it was exactly 9 o'clock in the morning at the
ship, by a correct celestial observation. In what part of
the ocean was the ship ?

7. When it is noon at London, what inhabitants of the
earth have midnight ?

8. When it is ten o'clock in the morning at London,
where is it ten o'clock in the evening ?

PROBLEM XX.

To find the suns longitude (commonly called tJie sun's place
in tJie ecliptic] and his declination.

RULE. Look for the given day in the circle of months
on the horizon, against which, in the circle of signs, are
the sign and degree in which the sun is for that day.
Find the same sign and degree in the ecliptic on the sur-
face of the globe ; bring the degree of the ecliptic, thus
found, to that part of the brass meridian which is num-
bered from the equator towards the poles, its distance
from the equator reckoned on the brass meridian, is the
sun's declination.

This problem may be performed by tJie celestial globe,
using the same rule.

OR, BY THE ANALEMMA.*

Bring the analemma to that part of the brass meridian
which is numbered from the equator towards the poles,

* The Analemma is properly an orthographic projection of the
sphere* on the plane of the meridian ; but what is called the Analemma
on the globe is a narrow slip of paper, the length of which is equal
to the breadth of the torrid zone. It is pasted on some vacant place

210 PROBLEMS PERFORMED BY Part III.

and the degree on the brass meridian, exactly above the
day of the month, is the sun's declination. Turn the
globe till a point of the ecliptic, corresponding to the day
of the month, passes under the degree of the sun's de-
clination, that point will be the sun's longitude or place
for the given day. If the sun's declination be north) and
increasing, the sun's longitude will be somewhere between
Aries and Cancer. If the declination be decreasing, the
longitude will be between Cancer and Libra. If the sun's
declination be south, and increasing, the sun's longitude
will be between Libra and Capricorn ; if the declination
be decreasing, the longitude will be between Capricorn
and Aries.

The sun's longitude is given in the third page and declination in the
second page of every month in the Nautical Almanac, for every day in
that month ; they are likewise given in White's Ephemeris, ,for every
day in the year.

EXAMPLES. 1. What is the sun's longitude and de-
clination on the 15th of May 1844 ?

Answer. The sun's longitude is 54° 42' or 24° 42' in a , and de-
clination 18° 57'.

2. Required the sun's place and declination for the
following days ?

January 21.

May 18.

September 9.

February 7.

June 11.

October 16.

March 16.

July 11.

November 17.

April 8.

August 1.

December 1.

on the globe in the torrid zone, and* is divided into months, and days
of the months, corresponding to the sun's declination for every day in
the year. It is divided into two parts ; the right-hand part begins at
the winter solstice, or December 21st, and is reckoned upwards towards
the summer solstice, or June 21st, where the left-hand part begins,
which is reckoned downwards in a similar manner, or towards the
winter solstice. On CART'S globes the Analemma somewhat resem-
bles the figure 8. It appears to have been drawn in this shape for the
convenience of shewing the equation of time, by means of a straight
line which passes through the middle of it. The equation of time is
placed on the horizon of BARDIN'S globes.

Chap. I. THE TERRESTRIAL GLOBE. 211

PROBLEM XXI.

To place tfie globe in tJiesame situation WITH RESPECT TO
THE SUN, as our earth is at tJie EQUINOXES, at ttte
SUMMER SOLSTICE, and at the WINTER SOLSTICE, and
thereby to shew the comparative lengths of the longest
and shortest days.*

1. FOR THE EQUINOXES. Place the two poles of the
globe in the horizon : for at this time the sun has no de-
clination, being in the equinoctial in the heavens, which
is an imaginary line standing vertically over the equator
on the earth. Now, if we suppose the sun to be fixed,
at a considerable distance from the globe, vertically over
that point of the brass meridian which is marked o", it is
evident that the wooden horizon will be the boundary of
light and darkness on the globe, and that the upper hemi-
sphere will be enlightened from pole to pole.

Meridians, or lines of longitude, being generally drawn
on the globe through every 15 degrees of the equator, the
sun will apparently pass from one meridian to another in
an hour. If you bring the point Aries on the equator to
the eastern part of the horizon, the point Libra will be
in the western part thereof; and the sun will appear to be
setting to the inhabitants of London f and to all places
under the same meridian : let the globe be now turned
gently on its axis towards the east, the sun will appear
to move towards the west, and, as the different places

* In this problem, as in all others where the pole is elevated to the
sun's declination, the sun is supposed to be fixed, and the earth to
move on its axis from west to east. The author of this work has a little
brass ball made to represent the sun ; this ball is fixed upon a strong
wire, and when used, slides out of a socket like an acromatic telescope.
The socket is made to screw to the brass meridian (of any globe) over
the sun's declination, and the little brass ball representing the sun,
stands over the decimation, at a considerable distance from the globe.

t The meridian of London is here supposed to pass through the
equinoctial point Aries, as on the best modern globes.

212 PROBLEMS PERFORMED BY Part III.

successively enter the dark hemisphere, the sun will ap-
pear to be setting in the west. Continue the motion of
the globe eastward, till London comes to the western
edge of the horizon ; the moment it emerges above the
horizon, the sun will appear to be rising in the east. If
the motion of the globe on its axis be continued east-
ward, the sun will appear to rise higher and higher, and
to move towards the west ; when London comes to the
brass meridian, the sun will appear at its greatest height ;
and after London has passed the brass meridian, he will
continue his apparent motion westward, and gradually
diminish in altitude till London comes to the eastern
part of the horizon, when he will again be setting. Dur-
ing this revolution of the earth on its axis, every place on
its surface has been twelve hours in the dark hemisphere,
and twelve hours in the enlightened hemisphere ; con-
sequently the days and nights are , equal all over the
world ; for all the parallels of latitude are divided into two
equal parts by the horizon, and in every degree of lati-
tude there are six meridians between the eastern part of
the horizon and the brass meridian ; each of these me-
ridians answers to one hour, hence half the length of the
day is six hours, and the whole length twelve hours.

If any place be brought to the brass meridian, the num-
ber of degrees between that place and the horizon (reck-
oned the nearest way) will be the sun's meridian altitude.
Thus, if London be brought to the meridian, the sun
will then appear exactly south, and its altitude will be
38± degrees ; the sun's meridian altitude at Philadelphia
will be 50 degrees ; his meridian altitude at Quito 90 de-
grees ; and here, as in every place on the equator, as the
globe turns on its axis, the sun will be vertical. At the
Cape of Good Hope the sun will appear due north at noon,
and his altitude will be 55£ degrees. ^

2. FOR THE SUMMER SOLSTICE — The summer sol-
stice, to the inhabitants of north latitude, happens on the
21st of June, when the sun enters Cancer, at which time
his declination is 23° 28' north. Elevate the north pole
23^ degrees above the northern point of the horizon,
bring the sign of Cancer in the ecliptic to the brass me-

Chap. I. THE TERRESTRIAL GLOBE. 213

ridian, and over that degree of the brass meridian under
which this sign stands, let the sun be supposed to be fixed
at a considerable distance from the globe.

While the globe remains in this position, it will be
seen that the equator is exactly divided into two equal
parts, the equinoctial point Aries being in the western
part of the horizon, and the opposite point Libra in the
eastern part, and between the horizon and the brass me-
ridian (counting on the equator) there are six meridians,
each fifteen degrees, or an hour apart, consequently the
day at the equator is 12 hours long. From the equa-
tor northward as far as the arctic circle, the diurnal
arcs will exceed the nocturnal arcs ; that is, more than
one half of any of the parallels of latitude will be above
the horizon, and of course less than one half will be be-
low, so that the days are longer than the nights. All
the parallels of latitude within the Arctic circle will be
wholly above the horizon, consequently those inhabitants
will have no night. From the equator southward, as
far as the Antarctic circle, the nocturnal arcs will ex-
ceed the diurnal arcs ; that is, more than one half of
any one of the parallels of latitude will be below the
horizon, and consequently less than one half will be
above. All the parallels of latitude within the Antarctic
circle, will be wholly below the ..horizon, and the inha-
bitants, if any, will have twilight or dark night.

From a little attention to the parallels of latitude,
while the globe remains in this position, it will easily be
seen that the arcs of those parallels which are above
the horizon north of the equator, are exactly of the same
length as those below the horizon, south of the equator ;
consequently, when the inhabitants of north latitude have
the longest day, those in south latitude have the longest
night. It will likewise appear, that the arcs of those
parallels which are above the horizon, south of the equa-
tor, are exactly of the same length as those below the
horizon north of the equator ; therefore, when the inha-
bitants who are situated south of the equator have the
shortest day, those who live north of the equator have
the shortest night.

214- PROBLEMS PERFORMED BY Part III.

By counting the number of meridians, (supposing them
to be drawn through every fifteen degrees of the equator)
between the horizon and the brass meridian, on any
parallel of latitude, half the length of the day will be de-
termined in that latitude, the double of which is the
length of the day.

1. In the parallel of 20 degrees north latitude, there
are six meridians and two thirds more, hence the longest
day is 13 hours and 20 minutes ; and in the parallel of
20 degrees south latitude there are five meridians and
one third, hence the shortest day in that latitude is ten
hours and forty minutes.

2. In the parallel of 30 degrees north latitude, there
are seven meridians between the horizon and the brass
meridian, hence the longest day is 14 hours ; and in the
same degree of south latitude there are only five me-
ridians, hence the shortest day in that latitude is ten
hours.

3. In the parallel of 50 degrees north latitude there are
eight meridians between the horizon and the brass me-
ridian ; the longest day is therefore sixteen hours ; and
in the same degree of south latitude there are only four
meridians ; hence the shortest day is eight hours.

4. In the parallel of 60 degrees north latitude, there
are 9£ meridians from the horizon to the brass meridian,
hence the longest day is 18| hours ; and in the same de-
gree of south latitude, there are only 2| meridians, the
length of the shortest day is therefore 5£ hours.

By turning the globe gently round on its axis from west
to east, we shall readily perceive that the sun will be
vertical to all the inhabitants under the tropic of Cancer,
as the places successively pass the brass meridian.

If any place be brought to the brass meridian, the
number of degrees between that place and the horizon
(reckoned the nearest way) will shew the sun's meridian
altitude. Thus, at London, the sun's meridian altitude
will be found to be about 62 degrees ; at Petersburg 54£
degrees, at Madrid 73 degrees, &c. To the inhabitants
of these places the sun appears due south at noon. At
Madras the sun's meridian altitude will be 79£ degrees,

Chap, I. THE TERRESTRIAL GLOBE. 215

at the Cape of Good Hope 32 degrees, at Cape Horn 10J
degrees, &c. The sun will appear due north to the in-
habitants of these places at noon. If the southern
extremity of Spitzbergen, in latitude 76^ north, be
brought to that part of the brass meridian which is
numbered from the equator towards the poles, the sun's
meridian altitude will be 37 degrees, which is its greatest
altitude ; and if the globe be turned eastwards twelve
hours, or till Spitzbergen comes to that part of the
brass meridian which is numbered from the pole to-
wards the equator, the sun's altitude will be ten degrees,
which is its least altitude for the day given in the pro-
blem. It was shewn, in the foregoing part of the pro-
blem, that, when the sun is vertically over the equator in
the vernal equinox, the north pole begins to be en-
lightened, consequently the farther the sun apparently
proceeds in its course northward, the more day-light will
be diffused over the north polar regions, and the sun will
appear gradually to increase in altitude at the north
pole, till the 21st of June, when his greatest height is
23£ degrees ; he will then gradually diminish in height till
the 23d of September, the time of the autumnal equinox,
when he will leave the north pole, and proceed towards
the south ; consequently the sun has been visible at the
north pole for six months.

3. FOR THE WINTER SOLSTICE. — The winter solstice,
to the inhabitants of north latitude, happens on tke 21st
of December, when the sun enters Capricorn, at which
time his declination is 23° 28' south. Elevate the south
pole 23^ degrees above the southern point of the horizon,
bring the sign of Capricorn in the ecliptic to the brass
meridian, and over that degree of the brass meridian
under which this sign stands, let the sun be supposed to be
fixed at a considerable distance from the globe.

Here, as at the summer solstice, the days at the equatoi
will be twelve hours long, but the equinoctial point Aries
will be in the eastern part of the horizon, and Libra in
the western. From the equator southward, as far as the
Antarctic circle, the diurnal arcs will exceed the nocturnal
arcs. All the parallels of latitude within the Antarctic
circle will be wholly above the horizon. From the equa-

216 PROBLEMS PERFORMED BY Part III.

tor northward, the nocturnal arcs will exceed the
diurnal arcs. All the parallels of latitude within the
Arctic circle will be wholly below the horizon. The
inhabitants south of the equator will now have their
longest day, while those on the north of the equator will
have their shortest day.

As the globe turns on its axis from west to east, the
sun will be vertical successively to all the inhabitants
under the tropic of Capricorn. By bringing any place
to the brass meridian, and finding the sun's meridian
altitude (as in the foregoing part of the problem), the
greatest altitudes will be in south latitude, and the least
in the north; contrary to what they were before.
Thus, at London, the sun's greatest altitude will be
only 15 degrees, instead of 62; and its greatest altitude
at Cape Horn will now be 57%, degrees, instead of 10|, as
at the summer solstice; hence it appears, that the
difference between the sun's greatest and least meri-
dian altitude at any place in the temperate zone, is equal
to the breadth of the torrid zone, viz. 47 degrees, or
nore correctly 46° 56'. On the 23d of September,
when the sun enters Libra, that is, at the time of the
autumnal equinox, the south pole begins to be enlightened,
and, as the sun's declination increases southward, he
will shine farther over the south pole, and gradually
increase in altitude at the pole ; for, at all times, his alti-
tude at either pole is equal to his declination. On the
21 st. of December, the sun will have the greatest south
declination, after which his altitude at the south pole will
gradually diminish as his declination diminishes ; and on
the 21st of March, when the sun's declination is nothing,
he will appear to skim along the horizon at the south
pole, and likewise at the north pole ; the sun has there-
fore been visible at the south pole for six months.

Chap, I THE TERRESTRIAL GLOBE. 217

PROBLEM XXII.

To place the globe in the same situation, WITH RESPECT TO
THE POLAR STAR in the heavens, as our earth is to
the inhabitants of the equator, fyc. viz. to illustrate the
three positions of the sphere, RIGHT, PARALLEL and
OBLIQUE, so as to shew flie comparative length of the
longest and shortest days.*

1. FOR THE RIGHT SPHERE. The inhabitants who
live upon the equator have a right sphere, and the north
polar star appears always in (or very near) the horizon.
Pkice the two poles of the globe in the horizon, then the
north pole will correspond with the north polar star, and
all the heavenly bodies will appear to revolve round the
earth from east to west, in circles parallel to the equi-
noctial, according to their different declinations : one
half of the starry heavens will be constantly above the
horizon, and the other half below, so that the stars will
be visible for twelve hours, and invisible for the same
space of time; and, in the course of a year, an inhabitant
upon the equator may see all the stars in the heavens.
The ecliptic being drawn on the terrestrial globe, young
students are often led to imagine that the sun apparently
moves daily round the earth in the same oblique manner.
To correct this false idea, we must suppose the ecliptic
to be transferred to the heavens, where it properly points
out the sun's apparent annual path amongst the fixed
stars. The sun's diurnal path is either over the equator,
as at the time of the equinoxes, or in lines nearly parallel
"to the equator; this may be correctly illustrated by
fastening one end of a piece of packthread upon the point
Aries on the equator, and winding the packthread round

* In this problem, and in all others where the pole is elevated
to the latitude of a given place, the earth is supposed to be fixed, and
the sun to move round it from east to west. When the given place
is brought to the brass meridian, the wooden horizon is the true
rational horizon of that place, but it does not separate the en-
lightened part of the globe from the dark part, as in the preceding
problem.

218 PROBLEMS PERFORMED BY Part III.

the globe towards the right hand, so that one fold may
touch another, till you come to the tropic of Cancer :
thus you will have a correct view of the sun's apparent
diurnal path from the vernal equinox to the summer
solstice ; for, after a diurnal revolution, the sun does not
come to the same point of the parallel whence it departed,
out, according as it approaches to or recedes from the
tropic, is a little above or below that point. When the
sun is in the equinoctial, he will be vertical to all the in-
habitants upon the equator, and his apparent diurnal path
will be over that line : when the sun has ten degrees of
north declination, his apparent diurnal path will be from
east to west nearly along that parallel. When the sun
has arrived at the tropic of Cancer, his diurnal path in
the heavens will be along that line, and he will be vertical
to all the inhabitants on the earth in latitude 23° 28' north.
The inhabitants upon the equator will always have twelve
hours day and twelve hours night, notwithstanding the
variation of the sun's decimation from north to south, or
from south to north ; because the parallel of latitude
which the sun apparently describes for any day will
always be cut into two equal parts by the horizon.
The greatest meridian altitude of the sun will be 90°,
and the least 66° 32'. During one half of the
year, an inhabitant on the equator will see the sun
full north at noon, and during the other half it will be full
south.

2. FOR THE PARALLEL SPHERE. — The inhabitants
(if any) who live at the north pole have a parallel sphere,
and the north polar star in the heavens appears exactly
(or very nearly) over their heads. Elevate the north pole
ninety degrees above the horizon, then the equator will
coincide with the horizon, and all the parallels of latitude
will be parallel thereto. In the summer half-year, that
is, from the vernal to the autumnal equinox, the sun will
appear above the horizon, consequently the stars and
planets will be invisible during that period. When the
sun enters Aries, on the 21st March, he will be seen
by the inhabitants of the north pole (if there be any in-
habitants) to skim just along the edge of the horizon :
and as he increases in declination, he will increase in

Ckap.I. THE TERRESTRIAL GLOBE. 219

altitude, forming a kind of spiral course, as before described,
by wrapping a thread round the globe. The sun's altitude
at any particular hour is always equal to his declination.
The greatest altitude the sun can have is 23° 28', at
which time he has arrived at the tropic of Cancer ; after
which he will gradually decrease in altitude as his
declination decreases. When the sun arrives at the
sign Libra, he will again appear to skim along the
edge of the horizon, after which he will totally disappear,
having been above the horizon for six months. Though
the inhabitants at the north pole will lose sight of the sun
a short time after the autumnal equinox, yet the twilight
will continue for nearly two months ; for the sun will not
be 18° below the horizon till he enters the 20th of
Scorpio, as may be seen by the globe.

After the sun has descended 18° below the horizon,
all the stars in the northern hemisphere will become
visible, and appear to have a diurnal revolution
round the earth from east to west, as the sun appeared
to have when he was above the horizon. These stars will
not set during the winter half of the year ; and the
planets, when they are in any of the northern signs, will
be visible. The inhabitants under the north polar star have
the moon constantly above their horizon during fourteen
revolutions of the earth on its axis, and at every full
moon which happens, from the 23d of September to the
21st of March, the moon is in some of the northern
signs, and consequently visible at the north pole ; for
the sun being below the horizon at that time, the moon
must be above the horizon, because she is always in
that sign which is diametrically opposite to the sun at
the time of full moon.

When the sun is at his greatest depression below the
horizon, being then in Capricorn, the moon is at her
FIRST QUARTER in Aries : FULL in Cancer ; and at her
THIRD QUARTER in Libra : and as the beginning of
Aries is the rising point of the ecliptic, Cancer the high-
est, and Libra the setting point, the moon rises at her
FIRST QUARTER in Aries, is most elevated above the
horizon, and FULL in Cancer, and sets at the beginning
of Libra in her THIRD QUARTER ; having been visible

L 2

C220 PROBLEMS PERFORMED BY Part III.

for fourteen revolutions of the earth on its axis, viz.
during the moon's passage from Aries to Libra. Thus
the north pole is supplied one half of the winter time
with constant moon light in the sun's absence ; and the
inhabitants only lose sight of the moon from her THIRD
to her FIRST QUARTER, while she gives but little light,
and can be of little or no service to them.

3. FOR THE OBLIQUE SPHERE. Whenever the ter-
restrial globe is placed in a proper situation with respect
to the fixed stars, the pole must be elevated as many
degrees above the horizon as are equal to the latitude of
the given place, and the north pole of the globe must
point to the north polar star in the heavens ; for in sailing,
or travelling from the equator northward, the north polar
star appears to rise higher and higher. On the equator
it will appear in the horizon; in ten degrees of north
latitude it will be ten degrees above the horizon ; in
twenty degrees of north latitude it will be twenty degrees
above the horizon ; and so on, always increasing in altitude
as the latitude increases. Every inhabitant of the earth,
except those who live upon the equator, or exactly under
the north polar star, has an oblique sphere, viz. the
equator cuts the horizon obliquely. By elevating and
depressing the poles, in several problems, a young student
is sometimes led to imagine that the earth's axis moves
northward and southward just as the pole is raised or
depressed : this is a mistake, the earth's axis has no such
motion.* In travelling from the equator northward, our
horizon varies ; thus, when we are on the equator, the
northern point of our horizon is exactly opposite the north
polar star ; when we have travelled to ten degrees north
latitude, the north point of our horizon is ten degrees
below the pole, and so on : now, the wooden horizon on
the terrestrial globe is immovable, otherwise it ought to
be elevated or depressed, and not the pole ; but whether
we elevate the pole ten degrees above the horizon, or de-

1 The earth's axis has a kind of librating motion, called the nuta-
tion, but this cannot be represented by elevating or depressing the
pole.

Chap. I. THE TERRESTRIAL GLOBE. 221

press the north point of the horizon ten degrees below
the pole, the appearance will be exac.tly the same.

The latitude of London is about 51^ degrees north: if
London be brought to the brass meridian, and the north
pole be elevated 51£ degrees above the north point of
the wooden horizon, then the wooden horizon will be the
true horizon of London ; and, if the artificial globe be
placed exactly north and south by a mariner's compass, or
by a meridian line, it will have exactly the position which
the real y lobe has. Now, if we imagine lines to be drawn
througli every degree* within the torrid zone, parallel to
the equator, they will nearly represent the sun's diurnal
path on any given day. By comparing these diurnal
paths with each other, they will be found to increase in
length from the equator northward, and to decrease in
length from the equator southward ; consequently, when
the sun is north of the equator, the days are increasing
in length ; and when south of the equator, the days
are decreasing,. The sun's meridian altitude for any-
day may be found by counting the number of degrees
from the parallel in which the sun is on that day, towards
the horizon, upon the brass meridian ; thus, when the
sun is in that parallel of latitude which is ten degrees
north of the equator, his meridian altitude will be 48^ de-
grees. Though the wooden horizon be the true horizon
of the given place, yet it does not separate the en-
lightened hemisphere of the globe from the dark hemi-
sphere, when the pole is thus elevated. For instance,
when the sun is in Aries, and London at the meridian,
all the places on the globe above the horizon beyond
those meridians which pass through the east and west
points thereof, reckoning towards the north, are in dark-
ness, notwithstanding they are above the horizon : and all
places below the horizon, between those same meridians
and the southern point of the horizon, have day-light, not-
withstanding they are below the horizon of London.

* Such lines arc drawn on Adams' globes.
L3

222 PROBLEMS PERFORMED BY Part III.

PROBLEM XXIII.

Tlie month and day of the month being given, to find all
places of the earth where the sun is vertical on that day ;
those places where the sun does not set, and those places
where -he does not rise on the given day.

RULE. Find the sun's declination (by Problem XX.)
for the given day, and mark it on the brass meridian ;
turn the globe round on its axis from west to east, and
all the places which pass under this mark will have the
sun vertical on that day.

Secondly. Elevate the north or south pole, according
as the sun's declination is north or south, so many
degrees above the horizon as are equal to the suns
declination : turn the globe on its axis from west to
east ; then, to those places which do not descend below
the horizon, in that frigid zone near the elevated pole, the
sun does not set on the given day : and to those places
which do not ascend above the horizon, in that frigid
zone adjoining to the depressed pole, the sun does not
rise on the given day.

OR, BY THE ANALEMMA.

Bring the analemma to that part of the brass meridian
which is numbered from the equator towards the poles,
the degree directly above the day of the month, on the
brass meridian, is the sun's declination. Elevate the
north or south pole, according as the sun's declination is
north or south, so many degrees above the horizon as are
equal to the sun's declination ; turn the globe on its axis
from west to east, then to those places which pass under
the sun's declination, on the brass meridian the sun will
be vertical ; to those places (in that frigid zone near the
elevated pole) which do not go below the horizon, the
sun does not set ; and to those places (in that frigid zone
near the depressed pole) which do not come above the
horizon, the sun does not rise on the given day.

EXAMPLES. 1. Find all places of the earth where the

Chap. I. THE TERRESTRIAL GLOBE. 223

sun is vertical on the llth of May, those places in the
north frigid zone where the sun does not set, and those
places in the south frigid zone where he does not rise.

Answer. The sun is vertical at St. Anthony, one of the Cape Verd
Islands, the Virgin Islands, south of St. Domingo, Jamaica, Golconda,
&c. All the places within eighteen degrees of the north pole will have
constant day ; and those (if any) within eighteen degrees of the south
pole will have constant night.

2. Whether does the sun shine over the north or sou^n
pole on the 27th of October, to what places will he be
vertical at noon, what inhabitants of the earth will have
the sun below their horizon during several revolutions,
and to what part of the globe will the sun never set on
that day ?

3. Find all the places of the earth where the inhabit-
ants have no shadow when the sun is on their meridian on
the first of June.

4. What inhabitants of the earth have their shadows
directed to every point of the compass during a revolution
of the earth on its axis on the 15th of July ?

5. How far does the sun shine over the south pole on
the 14-th of November, what places in the north frigid
zone are in perpetual darkness, and to what places is the
sun vertical ?

6. Find all places of the earth where the moon will be
vertical on the 26th of June, 1845.* See p. 224. f

* To perform this example, find the moon's declination on the given
day in the Nautical Almanac, or White's Ephemeris, and mark it on
the brass meridian; all places passing under that degree of declination
will have the moon vertical, or nearly so, on the given day. The
editor of the present edition of Mr. Keith's Treatise on the Globes con-
ceives he should be altogether unpardonable were he to pass over in
silence the wonderful improvements which the Nautical Almanacs since
t/ieyear 1834 have received ; to explain the sense of which, he quotes the
following passage from page 7. of the preface to that very valuable
volume. " In the year 1830, reference was made by the Lords Com-
missioners of the Admiralty to the Astronomical Society to consider if
any and what improvements could be made in the NAUTICAL ALMANAC.
The council presented their report upon the subject in November of the
same year, which was immediately approved by their Lordships, and or-
dered to be carried into effect for the year 1834." To particularise the
numerous improvements this grand national work has received in conse-
quence of this judicious order of their Lordships (which has been so ably
executed by those highly talented gentlemen to whom this important
L 4

224- PROBLEMS PERFORMED BY Part III.

PROBLEM XXIV.
A place being given in tJie torrid zone, to find those two

days of the year on which the sun will be vertical at that

place.

RULE. Bring the given place to that part of the brass
meridian which is numbered from the equator towards the
poles, and mark its latitude ; turn the globe on its axis,
and observe what two points of the ecliptic pass under
that latitude : seek those points of the ecliptic in the circle
of signs on the horizon, and exactly against them, in the
circle of months, stand the days required.

OR, BY THE ANALEMMA.

Find the latitude of the given place (by Problem I.),
and mark it on the brass meridian ; bring the analemma
to the brass meridian, upon which, exactly under the lati-
tude, will be found the two days required.

EXAMPLES. 1. On what two days of the year will the
sun be vertical at Madras ?

Answer. On the 25th of April and on the 18th of August.
2. On what two days of the year is the sun vertical at
the following places ?

O'why'hee St. Helena Sierra Leone

Friendly Isles Rio Janeiro Vera Cruz

Straits of Macassar Quito Manilla

Penang Barbadoes Tinian Isle

Trincomale Port Bello Pelew Islands.

task was referred), would far exceed the limits of the present work ; as
a specimen, however, somewhat connected with the above Problem, the
editor begs to point out that the right ascension, and declination of
the moon, formerly given for noon and midnight only of each day, is
in the Nautical Almanac for 1834 given for every hour of the day with
the difference of declination for 10 minutes; an improvement which
merely requires to be pointed out in order to be duly appreciated by
every Nautical Astronomer. It is but justice, however, due to Mr.
Pond, individually, to state (for the information of those who may be
unacquainted with the fact), that the improvement above noticed was
to a certain extent anticipated by that gentleman in the introduction
into the Nautical Almanac for 1833 of the right ascension and de-
clination of the moon for everi/ third hour.

f The moon's declination at midnight on the 26th of June, 1 845,
by the Nautical Almanac, is 7° 8' 59". 8 N.

Chap. I. THE TERRESTRIAL GLOBE. 225

PROBLEM XXV.

The month and the day of the month being given (at any
place not in the frigid zones), to find what other day of
the year is of the same length.

RULE. Find the sun's place in the ecliptic for the
given day (by Problem XX.), bring it to the brass meridian,
and observe the degree above it ; turn the globe on its
axis till some other point of the ecliptic falls under the
same degree of the meridian : find this point of the eclip-
tic on the horizon, and directly against it you will find the
day of the month required.

This Problem may be performed by the celestial globe in the same manne*.
OR, BY THE ANALEMMA.

Look for the given day of the month on the analemma,
and adjoining to it you will find the required day of the
month.

OR, WITHOUT A GLOBE.

Any two days of the year which are of the same length,
will be an equal number of days from the longest or
shortest day. Hence, whatever number of days the given
day is before the longest or shortest day, just so many
days will the required day be after the longest or shortest
day, et contra.

EXAMPLES. 1. What day of the year is of the same
length as the 25th of April ?

Answer. The 18th of August.

2. What day of the year is of the same length as the
25th of May ?

3. If the sun rise at four o'clock in the morning at
London on the 17th of July, on what other day of the
year will it rise at the same hour ?

4. If the sun set at seven o'clock in the evening at
London on the 24-th of August, on what other day of the
year will it set at the same hour ?

5. If the sun's meridian altitude be 90° at Trincomale,
in the Island of Ceylon, on the 12th of April, on what

L 5

226 PROBLEMS PERFORMED BY Part 111.

other day of the year will the meridian altitude be the
same?

6. If the sun's meridian altitude at London on the 25th
of April be 51° 35', on what other day of the year will
the meridian altitude be the same ?

7. If the sun be vertical at any place on the 15th of April,
how many days will elapse before he is vertical a second
time at that place ?

8. If the sun be vertical at any place on the 20th of
August, how many days will elapse before he is vertical a
second time at that place ?

PROBLEM XXVI.

TJie month, day, and hour of the day being given, to find
where the sun is vertical at that instant.

RULE. Find the sun's declination (by Problem XX.),
and mark it on the brass meridian ; bring the given place
to the brass meridian, and set the index of the hour-circle
to the given time, turn the globe on its axis until the index
points to noon ; the place immediately under the sun's de-
clination is that to which the sun is vertical at the proposed
time.

EXAMPLES. 1. When it is forty minutes * past six
o'clock in the morning at London on the 25th of April,
where is the sun vertical ?

Answer. Madras.

2. When it is four o'clock in the afternoon at London
on the 18th of August, where is the sun vertical ?

Answer. Barbadoes.

3. When it is three o'clock in the afternoon at London
on the 4th of January, where is the sun vertical ?

4. When it is three o'clock in the morning at London
on the llth of April, where is the sun vertical ?

5. When it is thirty-seven minutes past one o'clock in
the afternoon at the Cape of Good Hope on the 5th of
February, where is the sun vertical ?

* The hour .circles in general are not divided into parts less than a
quarter of an hour, but in setting the index the odd minutes may easily
be allowed for with sufficient exactness for all practical purposes. En".

Chap. 1. THE TERRESTRIAL GLOBE. 227

6. When it is eleven minutes past one o'clock in the
afternoon at London on the 29th of April, where is the
sun vertical ?

7. When it is twenty minutes past five o'clock in the
afternoon at Philadelphia on the 18th of May, where is
the sun vertical ?

8. When it is nine o'clock in the morning at Calcutta
on the llth of April, where is the sun vertical?

PROBLEM XXVII.

The month, day, and hour of the day at any place being
given, to find all those places of the earth where the sun
is rising, those places where the sun is setting, those places
that have noon, that particular place where the sun is
vertical, those places that have morning twilight, those
places that have evening twilight, and those places that
have midnight.

. RULE. Find the sun's declination (by Problem XX.),
and mark it on the brass meridian ; elevate the north or
south pole, according as the sun's declination is north or
south, so many degrees above the horizon as are equal to
the sun's declination ; bring the given place to the brass
meridian, and set the index of the hour-circle to the given
hour ; turn the globe on its axis until the index points to
noon ; then all places along the western edge of the horizon
have the sun rising ; those places along the eastern edge
have the sun setting; those under the brass meridian
above the horizon, have noon ; that particular place which
stands under the sun's declination on the brass meridian,
has the sun vertical; all places below the western edge
of the horizon, within eighteen degrees, have morning
twilight ; those places which are below the eastern edge
of the horizon, within eighteen degrees, have evening
twilight ; all places under the brass meridian below the
horizon, have midnight ; all the places above the horizon
have day, and those below it have night or twilight.

228 PROBLEMS PERFORMED BY Part III,

EXAMPLES. 1. When it is fifty-two minutes past four
o clock * in the morning at London on the 5th of March,
find all places of the earth where the sun is rising, setting,
&c. &c.

Answer. The sun is rising at the western part of the White Sea,
Petersburgh, the Morea in Turkey, &c.

Setting at the eastern coast of Kamtschatka, Jesus Island, Palmer-
ston Island, &c. between the Friendly and Society Islands, &c.

Noon at the Lake Baikal, in Irkoutsk, Cochin China, Cambodia,
Sun da Islands, &c.

Vertical, at jBatavia.

Morning twilight at Sweden, part of Germany, the southern part of
Italy, Sicily, the western coast of Africa along the ^Ethiopian Ocean.
&c.

Evening twilight at the north-west extremity of North America, the
Sandwich Islands, Society Islands, &c.

Midnight at Labrador, New York, western part of St. Domingo,
Chili, and the western coast of South America.

Day at the eastern part of Russia in Europe, Turkey, Egypt, the
Cape of Good Hope, and all the eastern part of Africa, almost the whole
of Asia, &c.

Night at the whole of North and South America, the western rart
of Africa, the British Isles, France, Spain, Portugal, &c.

2. When it is four o'clock in the afternoon at London
on the 25th of April, where is the sun rising, setting, &c.
&c.?

Answer. The sun will be rising at O'why'hee, &c. ; setting at the
Cape of Good Hope, &c. it will be noon at Buenos Ayres, &c. : the
sun will be vertical at Barbadoes ; and, following the directions in the
Problem, all the other places are readily found.

3. When it is ten o'clock in the morning at London on
the longest day, to what countries is the sun rising, setting,
£c. &c.?

4. When it is ten o'clock in the afternoon at Botany
Bay on the 15th of October, where is the sun rising,
setting, &c. &c. ?

5. When it is seven o'clock in the morning at Washing-
ton on the 17th of February, where is the sun rising, set-
ting, &c. &c. ?

6. When it is midnight at the Cape of Good Hope on
the 27th of July, where is the sun rising, setting, &c. &c.?

See note to Problem 26.

Cliap. I. THE TERRESTRIAL GLOBE. 229

PROBLEM XXVIII.

To find tJie time of the sun's rising and setting, and length
of the day and night, at any place not in the frigid zones.

RULE. Find the sun's declination (by Problem XX.),
and elevate the north or south pole, according as the
declination is north or south, so many degrees above the
horizon as are equal to the sun's declination; bring the
given place to the brass meridian, and set the index of
the hour-circle to twelve; turn the globe till the given
place comes to the eastern semicircle of the horizon, and
the index * will show the time of the sun's rising, turn the
globe till the given place comes to the western edge of the
horizon and the index will shew the time of his setting, or
either of these taken from 12 will give the other, because
the sun is an equal time above the horizon, both before
and after 12. Double the time of the sun's setting gives
the length of the day, and double the time of rising gives
the length of the night.

By the same rule, the length of the longest day, at all places not in
the frigid zones, may be readily found: for the longest day at all
places in north latitude is on the 21st of June, or when the sun enters
Cancer ; and the longest day at all places in south latitude is on the
21st of December, or when the sun enters the sign Capricorn.

OR,

Find the latitude of the given place, and elevate the
north or south pole, according as the latitude is north or
south, so many degrees above the horizon as are equal to
the latitude ; find the sun's place in the ecliptic (by Pro-
blem XX.), bring it to the brass meridian, and set the
index of the hour-circle to twelve ; turn the globe till the
sun's place come to the eastern semicircle of the horizon,
and the index will show the time of the sun's rising ; turn
the globe, the sun's place comes to the western edge of

* If the hour circle has a double row of figures, it will show the
time of the sun's rising and setting both at once. — ED.

230 PROBLEMS PERFORMED BY Part III.

the horizon, and the index will show the time of his setting ;
then, as before, double the time of setting gives the length
of the day, and double the time of rising gives the length
of the night.

OR, BY THE ANALEMMA.;

Find the latitude of the given place, and elevate the
north or south pole, according as the latitude is north or
south, the same number of degrees above the horizon ;
bring the middle of the analemma to the brass meridian,
and set the index of the hour-circle to twelve ; turn the
globe till the day of the month on the analemma comes to
the eastern or western semicircle of the horizon, and the
index will show the time of the sun's rising, setting, &c. as
above.

EXAMPLES. 1. What time does the sun rise and set at
London on the 1st of June, and what is the length of the
day and night ?

Answer. The sun sets at 8 min. past 6, and rises at 54 min. past 3 :
the length of the day is 16 hours 12 minutes, and the length of the
night 7 hours 48 minutes. The learner will readily perceive that if
the time at which tbe sun rises be given, the time at which it sets, toge-
ther with the length of the day and night, may be found without a
globe ; if the length of the day be given, the length of the night and
the time the sun rises and sets may be found ; if the length of the
night be given, the length of the day and the time the sun rises and
sets are easily known.

2. At what time does the sun rise and set at the follow-
ing places, on the respective days mentioned, and what is
the length of the day and night?

London, 17th of May
Gibraltar, 22d of July
Edinburgh, 29th January
Botany Bay, 20th February
Pekin, 20th of April

Cape of Good Hope, 7 Dec.
Cape Horn, 29th January
Washington, 15th Decem.
Petersburgh, 24th October
Constantinople, 18th Aug.

3. Find the time the sun rises and sets at every place
on the surface of the globe on the 21st of March, and like-
wise on the 23d of September.

4. Required the length of the longest day and shortest
night at the following places :

Chap.l. THE TERRESTRIAL GLOBE. 231

London Paris Pekin

Petersburgh Vienna Cape Horn

Aberdeen Berlin Washington

Dublin Buenos Ayres Cape of Good Hope

Glasgow Botany Bay Copenhagen.

5. Required the length of the shortest day and longest
night at the following places :

London Lima Paris

Archangel Mexico O'why'hee

•O Taheitee St. Helena Lisbon

Quebec Alexandria Falkland islands.

6. How much longer is the 21st of June at Petersburgh
than at Alexandria ?

7. How much longer is the 21st of December at Alex-
andria than at Petersburgh ?

8. At what time does the sun rise and set at Spitzbergen
on the 5th of April ?

PROBLEM XXIX.

The length of the day at any place, not in the friQid zones,
being given, to Jind the sun's declination and tJie day of
the month.

RULE. Bring the given place to the brass meridian
and set the index to twelve ; turn the globe eastward *
till the index has passed over as many hours as are equal
to half the length of the day ; keep the globe from re-
volving on its axis, and elevate or depress one of the poles
till the given place exactly coincides with the eastern
semicircle of the horizon; the distance of the elevated
pole from the horizon will be the sun's declination : mark
the sun's declination, thus found, on the brass meridian :
turn the globe on its axis, and observe what two points
of the ecliptic pass under this mark ; seek those points
in the circle of signs on the horizon, and exactly against
them, in the circle of months, stand the days of the months
required.

* The globe may be turned either eastward or westward : the latter
is to be preferred, especially when the hour circle has but one row of
figures, as the hour of sunsetting is at once shown, which is just half
the length of the day En.

232 PROBLEMS PERFORMED BY Part III.

OR,

Bring the meridian passing through Libra* to coin-
cide with the brass meridian, elevate the pole to the
latitude of the place, and set the index of the hour-
circle to twelve ; turn the globe eastward till the index
has passed over as many hours as are equal to half the
length of the day, and mark where the meridian passing
through Libra is cut by the eastern semicircle of the
horizon ; bring this mark to the brass meridian -|-, and
the degree above it is the sun's decimation ; with which
proceed as above. J

OR, BY THE ANALEMMA.

Bring the middle of the analemma to the brass meri-
dian, elevate the pole to the latitude of the place, and
set the index of the hour-circle to twelve ; turn the globe
eastward till the index has passed over as many hours
as are equal to half the length of the day ; the two days,
on the analemma, which coincide with that point of the
meridian passing through the middle of the analemma
which is cut by the eastern semicircle of the horizon, will
be the days required ; and, by bringing the analemma to
the brass meridian, the sun's declination will stand exactly
above these days.

EXAMPLES. 1. What two days in the year are each
sixteen hours long at London, and what is the sun's
declination ?

Answer. The 24th of May and the 17th of July. The sun's de-
clination is about 21° north.

2. What two days of the year are each fourteen hours
long at London ?

3. On what t\vo days of the year does the sun set at
half-past seven o'clock at Edinburgh ?

* Any meridian will answer the purpose, and the globe may be
turned either eastward or westward.

f If Adams' globes be used, the meridian passing through Libra
is graduated like the brass meridian, and the declination is found at
once.

| If Newton's globes be used, the graduated meridian is that which
passes through Cancer. — ED.

Chap. I. THE TERRESTRIAL GLOBE. 233

4. On what two days of the year does the sun rise at
four o'clock at Petersburg?

5. What two nights of the year are each ten hours long
at Copenhagen ?

6. What day of the year at London is sixteen hours and
a half long ?

PROBLEM XXX.

To find the length of the longest day at any place in the
north* frigid zone.

RULE. Bring the given place to the northern point of
the horizon (by elevating or depressing the pole), and
observe its distance from the north pole on the brass
meridian; count the same number of degrees on the
brass meridian from the equator, towards the north pole,
and notice the degree ; then turn the globe on its axis,
and observe what two points of the ecliptic pass under the
said degree ; find those points of the ecliptic in the circle
of signs on the horizon, and exactly against them, in the
circle of months, you will find the days on which the
longest day begins and ends. The date of the day that
precedes the 21st of June is that on which the longest
day begins at the given place, and the date of the day that
follows the 21st of June is that on which the longest day
ends : the time between these days is the length of the
longest day.

OR, BY THE ANALEMMA.

* The south frigid zone being uninhabited (at least we know of no
inhabitants), the Problem is not applied to that zone, however, the
rule is general, reading south for north, and 21st of December fur the
21st of June.

234< PROBLEMS PERFORMED BY Part III.

EXAMPLES. 1. What is the length of the longest day
at the North Cape, in the island of Maggeroe, in latitude
71° 30' north ?

-Answer. The place is 1 85° from the pole ; the longest day begins
on the 14th of May, and ends on the 30th of July ; the day is there-
fore seventy-seven days long, that is, the sun does not set during
seventy-seven revolutions of the earth on its axis.

2. What is the length of the longest day in the north
of Spitzbergen, and on what days does it begin and end ?

3. What is the length of the longest day at the
northern extremity of Nova Zembla ?

4. What is the length of the longest day at the north
pole, and on what days does it begin and end ?

PROBLEM XXXI.

To find the length of the longest night at any place in the
north * frigid zone.

RULE. Bring the given place to the northern point
of the horizon (by elevating or depressing the pole), and
observe its distance from the north pole on the brass
meridian ; count the same number of degrees on the
brass meridian from the equator towards the south pole,
and mark the place where the reckoning ends ; turn the
globe on its axis, and observe what two points of the
ecliptic pass under the above mark ; find those points of
the ecliptic in the circle of signs on the horizon, and
exactly against them, in the circle of months, you will
find the days on which the longest night begins and
ends. The day preceding the 21st of December is that
on which the longest night begins at the given place, and
the day following the 21st of December is that on which
the longest night ends : the time between these days is
the length of the longest night.

* This problem is equally applicable to any place in the south frigid
zone, and the rule will be general by reading south for north, and the
contrary ; likewise, instead of the 21st of December read the 21st of
June.

Chap. I. THE TERRESTRIAL GLOBE. 235

OR, BY THE ANALEMMA.

Mark the brass meridian as directed in the foregoing
method, then bring the analemma to the brass meridian,
and the two days which stand under the above mark
will point out the beginning and end of the longest night.
EXAMPLES. 1. What is the length of the longest nighl
at the North Cape, in the island of Maggeroe, in latitude
71° 30' north ?

Answer. The place is 18^° from the pole : the longest night begins
on the 16th of November, and ends on the 27th of January: the night
is therefore seventy-three days long, that is, the sun does not rise
during seventy-three revolutions of the earth on its axis.

2. What is the length of the longest night at the north
of Spitzbergen ?

3. The Dutch wintered in Nova Zembla, latitude 76
degrees north, in the year 1596 ; on what day of the
month did they lose sight of the sun ; on what day of the
month did he appear again ; and how many days were
they deprived of his appearance, setting aside the effect
of refraction ?

4. For how many days are the inhabitants of the north-
ernmost extremity of Russia deprived of a sight of the
sun?

PROBLEM XXXII.

To find the number of days which the sun rises and sets at
any place in the north* frigid zone.

RULE. Bring the given place to the northern point
of the horizon (by elevating or depressing the pole), and
observe its distance from the north pole on the brass me-
ridian ; count the same number of degrees on the brass
meridian from the equator towards the poles northward
and southward, and make marks where the reckoning
ends ; observe what two points of the ecliptic nearest to

* The same might be found for a place in the south frigid zone,
were that zone inhabited.

236 PROBLEMS PERFORMED BY Part llj.

Aries pass under the above marks ; these points will
show (upon the horizon) the end of the longest night and
the beginning of the longest day ; during the time be-
tween these days the sun will rise and set every twenty-
four hours ; next observe what two points of the ecliptic,
nearest to Libra, pass under the marks on the brass me-
ridian ; find these points, as before, in the circle of signs,
and against them you will find the day on which the
longest day ends at the given place, and the day on which
the longest night begins ; during the time between these
days the sun will rise and set every twenty-four hours.

OR,

Find the length of the longest day at the given place
(by Prob. XXX.> and the length of the longest night
(by Prob. XXXI.), add these together, and subtract the
sum from 365 days, the length of the year; the remainder
will show the number of days which the sun rises and sets
at that place.

OR, BY THE ANALEMMA.

Find how many degrees the given place is from the
north pole, and mark those degrees upon the brass me-
ridian on both sides of the equator ; observe what four
days on the analemma stand under the marks on the
brass meridian ; the time between those two days on the
left hand part of the analemma (reckoning towards the
north pole) will be the number of days on which the
sun rises and sets, between the end of the longest night
and the beginning of the longest day ; and the time be-
tween the two days on the right-hand part of the analem-
ma (reckoning towards the south pole) will be the number
of days on which the sun rises and sets, between the end
of the longest day and the beginning of the longest night.

EXAMPLES. 1. How many days in the year does the
sun rise and set at the North Cape, in the island of Mag-
geroe, in latitude 71° 30' north ?

Answer. The place is 18i° from the pole, the two points in the
ecliptic, nearest to Aries, which pass under 18i° on the brass meri-

Chap. I. THE TERRESTRIAL GLOBE. 237

dian, are 8° in aa, answering to the 27th of January, and 24° in g ,
answering to the 14th of May. Hence the sun rises and sets for 107
days, viz. from the end of the longest night, which happens on the
27th of January, to the beginning of the longest day, which happens
on the 14th of May. Secondly, the two points in the ecliptic nearest
to Libra, which pass under 18^° on the brass meridian, are 8° in Q,
answering to the 30th of July, and 24° in m, answering to the 1 5th
of November. Hence the sun rises and sets for 108 days, viz. from
the end of the longest day, which happens on the 30th of July, to the
beginning of the longest night, which happens on the 15th of Novem-
ber j so that the whole time of the sun's rising and setting is 215 days.

OB, THUS:

The length of the longest day, by Example 1st, Prob. XXX. is 77
days; the length of the longest night, by Example 1st, Prob. XXXI.
is 73 days ; the sum of these is 150, which, deducted from 365, leaves
215 days as above.

2. How many days in the year does the sun rise and
set at the north of Spitzbergen ?

3. How many days does the sun rise and set at Green-
land, in latitude 75° north ?

4. How many days does the sun rise and set at the
northern extremity of Russia in Asia ?

PROBLEM XXXIII.

To find in what degree of north latitude, on any day between
the 21st of March and the 21 st of June, or in what degree
of south latitude, on any day between the 23d of September
and tiie 21st of December, the sun begins to shine con-
stantly without setting ; and also in what latitude in the
opposite hemisphere he begins to be totally absent.

RULE. Find the sun's declination (by Problem XX.),
and count the same number of degrees from the north
pole towards the equator, if the declination be north, or
from the south pole, if it be south, and mark the point
where the reckoning ends ; turn the globe on its axis,
and all places passing under this mark are those in which
the sun begins to shine constantly without setting at that
time : the same number of degrees from the contrary pole
will point out ell the places where twilight or total dark-
ness begins.

EXAMPLES. 1. In what latitude north, and at what

238 PROBLEMS PERFORMED B¥ Part III.

places, does the sun begin to shine without setting during
several revolutions of the earth on its axis, on the 14th of
May?

Answer. The sun's declination is 18^° north, therefore all places hi
latitude 71^° north will be the places sought, viz. the North Cape in
Lapland, the southern part of Nova Zembla, Icy Cape, &c.

2. In what latitude south does the sun begin to shine
without setting on the 18th of October, and in what lati-
tude north does he begin to be totally absent ?

Answer. The sun's declination is 10° south, therefore he begins to
shine constantly in latitude 80° south, where there are no inhabitants
known, and to be totally absent in latitude 80° north, viz. at Spitz-
bergen.

3. In what latitude does the sun begin to shine without
getting on the 20th of April ?

4. In what latitude north does the sun begin to shine
without setting on the 1st of June, and in what degree of
south latitude does he begin to be totally absent ?

PROBLEM XXXIV.

Any number of days, not exceeding 182, being given, to
find the parallel of north latitude in which the sun does
not set for that time.

RULE. Count half the number of days from the 21st
of June on the horizon, eastward or westward, and oppo-
site to the last day you will find the sun's place in the
circle of signs : look for the sign and degree on the eclip-
tic, which bring to the brass meridian, and observe the
sun's declination ; reckon the same number of degrees
from the north pole (on that part of the brass meridian
which is numbered from the equator towards the poles),
and you will have the latitude sought.

EXAMPLES. 1. In what degree of north latitude, and
at what places, does the sun continue above the horizon
for seventy-seven days ?

Answer. Half the number of days is 381, an(i if reckoned back-
ward, or towards the east, from the 21st of June, will answer to the
14th of May ; and if counted forward, or towards the west, will answer
to the 30th of July ; on either of which days the sun's declination is
18§ degrees north, consequently the places sought are 18£ degrees
from the north pole, or in latitude 71f degrees north ; answering to

Chap. I. THE TERRESTRIAL GLOBE. 239

the North Cape in Lapland, the south part of Nova Zembla, Icy
Cape, &c.

2. In what degree of north latitude is the longest day
134 days, or 3216 hours in length ?

s 3. In what degree of north latitude does the sun con-
tinue above the horizon for 2160 hours ?

4. In what degree of north latitude does the sun con-
tinue above the horizon for 1152 hours ?

PROBLEM XXXV.

To find the beginning, end, and duration of twilight at
any given place on any given day.

RULE. Find the sun's declination for the given day
(by Problem XX.), and elevate the north or south pole
according as the declination is north or south, so many
degrees above the horizon as are equal to the sun's de-
clination ; screw the quadrant of altitude on the brass
meridian, over the degree of the sun's declination ; bring
the given place to the brass meridian, and set the index
of the hour-circle to twelve : turn the globe eastward till
the given place comes to the horizon, and the hours passed
over by the index will show the time of the sun's setting,
or the beginning of evening twilight: continue the motion
of the globe eastward, till the given place coincides with
18° on the quadrant of altitude below* the horizon, and
the hours passed over by the index, from 12, will show
when evening twilight ends. The time when evening
twilight ends, subtracted from 12, will show the beginning
of morning twilight, which is of the same length as the
evening.

OR, THUS :

Elevate the north or south pole, according as the lati-
tude of the given place is north or south, so many degrees
above the horizon as are equal to the latitude ; find the
sun's place in the ecliptic, bring it to the brass meridian,
set the index of the hour-circle to twelve, and screw the

* The quadrant of altitude belonging to our modern globes is
always graduated to 18 degrees below the horizon.

240 PROBLEMS PERFORMED BY Part III.

quadrant of altitude upon the brass meridian over the
given latitude: turn the globe westward on its axis till
the sun's place comes to the western edge of the horizon,
and the hours passed over by the index will shew the
time of the sun's setting, or the beginning of evening
twilight ; continue the motion of the globe westward till
the sun's place coincides with 18° on the quadrant of al-
titude below the horizon, the time passed over by the in-
dex of the hour-circle, from the time of the sun's setting,
will shew the duration of evening twilight.

Oil, BY THE ANALEMMA.

Elevate the pole to the latitude of the place, as above,
and screw the quadrant of altitude upon the brass meri-
dian over the degree of latitude ; bring the middle of the
analemma to the brass meridian, and set the index of the
hour-circle to twelve ; turn the globe westward till the
given day of the month, on the analemma, comes to the
western edge of the horizon, and the hours passed over
by the index will shew the time of the sun's setting, or
the beginning of evening twilight : continue the motion
of the globe westward till the given day of the month
coincides with 18° on the quadrant below the horizon, the
time passed over by the index, from the time of the sun's
setting, will shew the duration of evening twilight.

EXAMPLES. 1. Required the beginning, end, and
duration of morning and evening twilight at London on
the 19th of April?

Answer. The sun sets at two minutes past seven, and evening twi-
light ends at nineteen minutes past nine ; consequently morning twi-
light begins at (12h. — 9h. 19m. =) 2h. 41m. and ends at (12h. —
7h. 2m. = ) 4h. 58m. ; the duration of twilight is 2h. and 1 7 minutes.

2. What is the duration of twilight at London on the
23d of September, what time does dark night begin, and
at what time does day break in the morning ?

Answer. The sun sets at six o'clock, and the duration of twilight
is two hours ; consequently the evening twilight ends at eight o'clock,
and the morning twilight begins at four.

3. Required the beginning, end, and duration of
morning and evening twilight at London on the 25th of
August ?

Chap. I. THE TERRESTRIAL GLOBE. 24-1

4. Required the beginning, end, and duration of morn-
ing and evening twilight at Edinburgh on the 20th of
February ?

5. Required the beginning, end, and duration of morn-
ing and evening twilight at Cape Horn on the 20th of
February ?

6. Required the beginning, end, and duration of morn-
ing and evening twilight at Madras on the 15th of June?

PROBLEM XXXVI.

To find the beginning, end, and duration of constant day
or twilight at any place.

RULE. Find the latitude of the given place, and add
18° to that latitude ; count the number of degrees corres-
pondent to the sum, on that part of the brass meridian
which is numbered from the pole towards the equator,
mark where the reckoning ends, and observe what two
points of the ecliptic pass under the mark * ; that point
wherein the sun's declination is increasing will shew on
the horizon the beginning of constant twilight ; and that
point wherein the sun's declination is decreasing, will shew
the end of constant twilight.

EXAMPLES. 1. When do we begin to have constant
day or twilight at London, and how long does it continue ?

Answer. The latitude of London is 51^ degrees north, to which
add 18 degrees, the sum is 69^, the two points of the ecliptic which
pass under 69 ^ are two degrees in IT, answering to the 22d of May,
and 29 degrees in 25, answering to the 21st of July ; so that, from the
22d of May to the 21st of July the sun never descends 18 degrees
below the horizon of Lorxlon.

2. When do the inhabitants of the Shetland islands
cease to have constant day or twilight ?

3. Can twilight ever continue from sun-set to sun-rise
at Madrid ?

* If, after 18 degrees be added to the latitude, the distance from
the pole will not reach the ecliptic, there will be no constant twilight
at the given place, viz. to the given latitude add 1 8 degrees, and sub-
tract the sum from 90, if the remainder exceed 23 § degrees, there can
be no constant twilight at the given place.

24-2 PROBLEMS PERFORMED BY Part II

4. When does constant day or twilight begin at Spitz-
bergen ?

5. What is the duration of constant day or twilight at
the North Cape in Lapland, and on what day, after their
long winter's night, do the sun's rays first enter the
atmosphere ?

PROBLEM XXXVII.
To find the duration of twilight at the north pole.

RULE. Elevate the north pole so that the equator may
coincide with the horizon; observe what point of the
ecliptic nearest to Libra passes under 18° below the
horizon, reckoned on the brass meridian, and find the day
of the month correspondent thereto ; the time elapsed
from the 23d of September to this time will be the dur-
ation of evening twilight. Secondly,' observe what point
of the ecliptic, nearest to Aries, passes under 18° below c
the horizon, reckoned on the brass meridian, and find the
day of the month correspondent thereto ; the time elapsed
from that day to the 21st of March will be the duration
of morning twilight.

EXAMPLE. What is the duration of twilight at the
north pole, and what is the duration of dark night there ?

Answer. The point of the ecliptic nearest to Libra which passes
under 18 degrees below the horizon, is 22 degrees in in> answering
to the 1 3th of November ; hence the evening twilight continues from
the 23d of September (the end of the longest day) to the 1 3th of
November (the beginning of dark night) being 51 days. The point of
the ecliptic nearest to Aries which passes under 1 8 degrees below the
horizon is 9 degrees in ;xs, answering to the 29th of January; hence
the morning twilight continues from the 29th of January to the 21st of
March (the beginning of the longest day) being 51 days. From the
23d of September to the 21st of March are 179 days, from which de-
duct 102 (=51 x 2), the remainder is 77 days, the duration of total
darkness at the north pole ; but, even during this short period, the
moon and the Aurora Borealis shine with uncommon splendour.

. I. THE TERRESTRIAL GLOBE. 24-3

PROBLEM XXXVIII.

To find in what climate any given place on the glebe is
situated.

RULE. 1. If the place be not in the frigid zone, find
the length of the longest day at that place (by Problem
XXVIII.) and subtract twelve hours therefrom ; the number
of half hours in the remainder will shew the climate.

2. If the place be in the frigid zone*, find the length
of the longest day at that place (by Problem XXX.),
and if that be less than thirty days, the place is in the
twenty-fifth climate, or the first within the polar circle.
If more than thirty and less than sixty, it is in the twenty-
sixth climate, or the second within the polar circle ; if
more than sixty, and less than ninety, it is in the twenty-
seventh climate, or the third within the polar circle, &c.

EXAMPLES. 1. In what climate is London, and what
other remarkable places are situated in the same climate ?

Answer. The longest day in London is 16^ hours, if we deduct 12
therefrom, the remainder will be 4| hours, or nine half hours ; hence
London is in the ninth climate north of the equator ; and as all places
in or near the same latitude are in the same climate, we shall find
Amsterdam, Dresden, Warsaw, Irkoutsk, the southern part of the
peninsula of Kamtschatka, Nootka Sound, the South of Hudson's Bay,
the north of Newfoundland, &c. to be in the same climate as London.
The learner is requested to turn to the note to Definition 69th, page 1 7.

* The climates between the polar circles and the poles were un-
known to the ancient geographers ; they reckoned only seven climates
north of the equator. The middle of the first northern climate they
made to pass through Meroe, a city of Ethiopia, built by Cambyses
on an island in the Nile, nearly under the tropic of Cancer ; the
second through Syene, a city of Thebais in Upper Egypt, near the
cataracts of the Nile ; the third through Alexandria ; the fourth
through Rhodes ; the fifth through Rome or the Helkspont ; the sixth
through the mouth of the Borysthenes or Dnieper; and the seventh
through the Riphhesan mountains, supposed to be situated near the
source of the Tanais or Don river. The southern parts of the earth
being in a great measure unknown, the climates received their names
from the northern ones, and not from particular towns or places.
Thus the climate, which was supposed to be at the same distance from
the equator southward as Meroe was northward, was called Antidia-
meroes, or the opposite climate to Meroe ; Aittidiasyenes was the oppo-
site climate to Syenes, &c.

M 2

244? PROBLEMS PERFORMED BY Part III.

2. Ill what climate is the North Cape in the island of
Maggeroe, latitude 71° 30' north ?

Answer* The length of the longest day is 77 days : these days
divided by 30 give two months for the quotient, and a remainder of
17 days ; hence the place is in the third climate within the polar circle,
or the 27th climate reckoning from the equator. The southern part of
Nova Zembla, the northern part of Siberia, James" Island, Baffin's
Bay, the northern part of Greenland, &c. are in the same climate.

3. In what climate is Edinburgh, and what other places
are situated in the same climate ?

4. In what climate is the north of Spitzbergen ? . ^ .

5. In what climate is Cape Horn ?

b". In what climate is Botany Bay, and what other
places are situated in the same climate ?

PROBLEM XXXIX.

To find the breadths of the several climates between the
equator and the polar circles.

RULE. For the northern climates. Elevate the north
pole 23J° above the northern point of the horizon ; bring
the sign Cancer to the meridian, and set the index to
twelve ; turn the globe eastward on its axis till the index
has passed over a quarter of an hour ; observe that
particular point of the meridian passing through Libra,
which is cut by the horizon, and at the point of inter-
section make a mark with a pencil ; continue the motion
of the globe eastward till the index has passed over
another quarter of an hour, and make a second mark ;
proceed thus till the meridian passing through Libra*
will no longer cut the horizon -j- ; the several marks brought
to the brass meridian will point out the latitude where
each climate ends. J

* On Adams' and Cary's globes the meridian passing through
Libra is divided into degrees, in the same manner as the brass meridian
is divided ; the horizon will, therefore, cut this meridian in the several
degrees answering to the end of each climate, without the trouble of
bringing it to the brass meridian, or marking the globe.

f On Newton's globes the meridian passing through Cancer is thus
divided. — ED.

| See a Table of the climates, with the method of constructing it,
at pages 18, and 19.

Chap. I. THE TERRESTRIAL GLOBE. 24-5

EXAMPLES. 1. What is the breadth of the ninth north
climate, and what places are situated within it ?

Answer. The breadth of the 9th climate is 2° 57' ; it begins m
latitude 49° 2' north, and ends in latitude 51° 59> north, and all
places situated within this space are in the same climate. The places
will be nearly the same as those enumerated in the first example to
the preceding problem.

2. What is the breadth of the second climate, and in
what latitude does it begin and end ?

3. Required the beginning, end, and breadth of the
fifth climate ?

4. What is the breadth of the seventh climate north
of the equator, in what latitude does it begin and end,
and what places are situated within it ?

5. What is the breadth of the climate in which
Petersburg is situated ?

6. What is the breadth of the climate in which Mount
Heckla is situated ?

PROBLEM XL.

To find that part of the equation of time which depends on,
the obliquity of the ecliptic.

RULE. Find the sun's place in the ecliptic, and bring
it to the brass meridian ; count the number of degrees
from Aries to the brass meridian, on the equator and on
the ecliptic ; the difference, reckoning four minutes of
time to a degree, is the equation of time. If the number
of degrees on the ecliptic exceed those on the equator,
the sun is faster than the clock ; but if the number of
degrees on the equator exceed those on the ecliptic,
the sun is slower than the clock.

246

PROBLEMS PERFORMED BY

Part III.

Note. The equation of time, or differ-
ence between the time shewn by a well-
regulated clock, and a true sun-dial,
depends upon two causes, viz. the ob-
liquity of the ecliptic, and the unequal
motion of the earth in its orbit. The
former of these causes may be explained
by the above Prpblem. If two suns were
to set off at the same time from the point
Aries, and move over equal spaces in
equal time, the one on the ecliptic, the
other on the equator, it is evident they
would never come to the meridian to-
gether, except at the time of the equi-
noxes, and on the longest and shortest
days. The annexed table shews how
much the sun is faster or slower than the
clock ought to be, so far as the variation
depends on the obliquity of the ecliptic
only. The signs of the first and third
quadrants of the ecliptic are at the top
of the table, and the degrees in these
signs on the left hand ; in any of these
signs the sun is faster than the clock.
The signs of the second and third quad-
rants are at the bottom of the table, and
the degrees in these signs at the right
hand ; in any of these signs the sun is
slower than the clock.

Thus, when the sun is in 20 degrees
of » or in > it is 9 minutes 50 seconds
faster than the clock, and, when the sun
is in 18 degrees of SB or vf, it is 6
minutes 2 seconds slower than the clock.

SUN faster than theCLOCK. in

iQu

:£r

3Qu

M. S.

0 0

M. S.

8 24

M. S.

8 46

0 208 35

8 36

0 408 45

8 25

1 08 54

8 14

1 199 3

8 1

1 399 11

7 49

25,

1 59!9 18

7 35

2 18 9 24

7 21

8
9

2 37 9 31
2 569 36

7 6
6 51

22
21

3 169 41

6 35

3 349 456 19

12'

3 539 496 2

13
14

4 119 515 45
4 299 535 27

17
16

15
16
17

4 47
5 4
5 21

9 54 5 9
9 55 4 50
9 554 31

15
14
13

5 389 544 12

5 549 5213 52

6 109 50J3 32

6 26'9 47

3 12

6 41

9 43

2 51

6 359 38

2 30

7 99 33

2 9

7 239 27

1 48

7 369 20

1 27

7 499 13

1 5

8 19 5

0 43

8 138 56

0 22

8 24

8 46

0 0

2Qu
4Qu

sxx

35
Vf

SUN slower than f/j* CLOCK**

. I. THE TERRESTRIAL GLOBE. 24?

EXAMPLES. 1. What is the equation of time on the
17th of July?

Answer. The degrees on the equator exceed the degrees on the
ecliptic by two : hence the sun is eight minutes slower than the
clock.*

2. On what four days of the year is the equation of
time nothing?

3. What is the equation of time dependant on the
obliquity of the ecliptic on the 27th of October ?

4. When the sun is in 189 of Aries, what is the equa-
tion of time ?

PROBLEM XLI.

To find the suns meridian altitude at any time of the year
at any given place.

RULE. Find the sun's declination, and elevate the pole
to that declination ; bring the given place to the brass
meridian, and count the number of degrees on the brass
meridian (the nearest) to the horizon ; these degrees
will shew the sun's meridian altitude, f

NOTE. The suns altitude may be found at any particular hour, in
thefottowiny manner.

Find the sun's declination, and elevate the pole to that declination ;
bring the given place to the brass meridian and set the index to 12 ;
then, if the given time be before noon, turn the globe westward as
many hours as the time wants of noon ; if the given time be past noon,
turn the globe eastward as many hours as the time is past noon. Keep
the globe fixed in this position, and screw the quadrant of altitude
on the brass meridian over the sun's declination ; bring the graduated
edge of the quadrant to coincide with the given place, and the number
of degrees between that place and the horizon will shew the sun's
altitude.

OR,

Elevate the pole so many degrees above the horizon as
are equal to the latitude of the place; find the sun's

* The learner will observe, that the equation of time here deter-
mined is not the true equation, as noted on the 7th circle on the
horizon of Bardin's globes ; the equation of time there given cannot
be determined by the globe. See the Table at the end of Problem
LXIV.

f See Problem XXI.

M 4}

PROBLEMS PERFORMED BY Part III.

place in the ecliptic, and bring it to that part of the
brass meridian which is numbered from the equator
towards the poles ; count the number of degrees contained
in the brass meridian between the sun's place and the
horizon, and they will show the altitude.*

To find the sun's altitude at any hour, see Problem XLIV.

OR, BY THE ANALEMMA.

Elevate the pole so many degrees above the horizon
as are equal to the latitude of the place ; find the day of
the month on the analemma, and bring it to that part of
the brass meridian which is numbered from the equator
towards the poles ; count the number of degrees con-
tained on the brass meridian between the given day of the
month and the horizon, and they will show the altitude, f

To find the sun's altitude at any hour, see Problem XLIV.

EXAMPLES. 1. What is the sun's meridian altitude at
London on the 21 st of June ?

Answer. 62 degrees.

2. What is the sun's meridian altitude at London on
the 21st of March?

3. What is the sun's least meridian altitude at London?

4. What is the sun's greatest meridian altitude at Cape
Horn?

5. What is the sun's meridian altitude at Madras on
the 20th of June ?

6. What is the sun's meridian altitude at Bencoolen on
the 15th of January?

* See Problem XXII.

f The sun's meridian altitude may be found by calculation as
follows : —

If the latitude of the place and the sun's declination be of the same
name, add the latter to the complement of the latitude : their sum will
be the sun's meridian altitude, but of a contrary name to the latitude.
Should the sum exceed 90°, its supplement will be the altitude and of
the same name with the latitude. When the latitude and declination are
•'of different names, the latter subtracted from the co-latitude will give
the sun's altitude of a contrary name to the latitude. If the declination
exceed the co-latitude, the sun will be so many degrees below the
horizon as are equal to the difference between them. — ED.

Chap. I. THE TERRESTRIAL GLOBE. 24-9

EXAMPLES to the note.

1. What is the sun's altitude at Madrid on the 24th of
August, at 1 1 o'clock in the morning ?

Answer. The sun's declination is llf degrees north ; by elevating
the north pole 11£ degrees above the horizon, and turning the globe
so that Madrid may be one hour westward of the meridian, the sun's
altitude will be found to be 57£ degrees.

2. What is the sun's altitude at London at 3 o'clock in
the afternoon on the 25th of April ?

3. What is the sun's altitude at Rome on the 16th of
January at 10 o'clock in the morning ?

4. Required the sun's altitude at Buenos Ayres on the
21st of December at two o'clock in the afternoon ?

PROBLEM XLIL

When it is midnight at any place in the temperate or torrid
zones, to find the sun's altitude at any place (on the same
meridian) in the north frigid zone, where the sun does
not descend below the horizon.

Rule. Find the sun's declination for the given day,
and elevate the pole to that declination ; bring the place
(in the frigid zone) to that part of the brass meridian
which is numbered from the north pole towards the equa-
tor, and the number of degrees between it and the horizon
will be the sun's altitude.

OR,

Elevate the north pole so many degrees above the hori-
zon as are equal to the latitude of the place in the frigid
zone ; bring the sun's place in the ecliptic to the brass
meridian, and set the index of the hour-circle to twelve ;
turn the globe on its axis till the index points to the
other twelve ; and the number of degrees between the
sun's place and the horizon, counted on the brass meridian
towards that part of the horizon marked north, will be the
sun's altitude.

M &

250 PROBLEMS PERFORMED BY Part III.

EXAMPLES. 1. What is the sun's altitude at the
North Cape in Lapland, when it is midnight at Alexan-
dria in Egypt on the 21st of June ?

Answer. 5 degrees.

2. When, it is midnight to the inhabitants of the island
of Sicily on the 22d of May, what is the sun's altitude at
the north of Spitzbergen, in latitude 80° north ?

3. What is the sun's altitude at the north-east of Nova
Zembla, when it is midnight at Tobolsk, on the 15th of
July?

4. What is the sun's altitude at the north of Baffin's
Bay, when it is midnight at Buenos Ayres, on the 28th of
May?

PROBLEM XLIII.
To find the suns amplitude at any place.

Elevate the pole so many degrees above the horizon as
are equal to the latitude of the given place ; find the sun's
place in the ecliptic, and bring it to the eastern semicircle
of the horizon ; the number of degrees from the sun's
place to the east point of the horizon will be the rising
amplitude ; bring the sun's place to the western semicircle
of the horizon, and the number of degrees from the sun's
place to the west point of the horizon will be the setting
amplitude.

OR, BY THE ANALEMMA.

Elevate the pole so many degrees above the horizon as
are equal to the latitude of the place ; bring the day of
the month on the analemma to the eastern semicircle of
the horizon : the number of degrees from the day of the
month to the east point of the horizon will be the rising
amplitude : bring the day of the month to the western
semicircle of the horizon, and the number of degrees from
the day of the month to the west point of the horizon will
be the setting amplitude.

EXAMPLES. 1. What is the sun's amplitude at Lon-
don on the 21st of June ?

Chap. I. THE TERRESTRIAL GLOBE. 251

Answer. 39° 48' to the north of the east, and 39° 48' to the north
of the west.

2. On what point of the compass does the sun rise and
set at London on the 17th of May ?

3. On what point of the compass does the sun rise and
set at the Cape of Good Hope on the 21st of December ?

4. On what point of the compass does the sun rise and
set on the 21st of March?

5. On what point of the compass does the sun rise and
set at Washington on the 21st of October ?

6. On what point of the compass does the sun rise and
set at Petersburgh on the 18th of December?

7. On December 22d, 1844, in latitude 31° 38' S. and
longitude 83° W., if the sun set on the S.W. point of the
compass, what is the variation ?

8. On the 15th of May 1846, if the sun rise E. by N.
in latitude 33° 15' N. and longitude 18° W., what is the
variation of the compass ?

PROBLEM XLIV.

To find the sun's azimuth and his altitude at anyplace, the
day and hour being given.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude on the brass meridian,
over that latitude ; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour circle to twelve ; then if the given time be before
noon, turn the globe eastward * as many hours as it wants
of noon ; but, if the given time be past noon ; turn the
globe westward as many hours as it is past noon, bring

* Whenever the pole is elevated for the latitude of the place, the
proper motion of the globe is from east to west, and the sun is on the
east side of the brass meridian in the morning, and on the west side
in the afternoon ; but when the pole is elevated for the sun's declin-
ation, the motion is from west to east, and the place is on the west
side of the meridian in the morning, and on the east side in the
afternoon.

M 6

252 PROBLEMS PERFORMED BY Part III.

the graduated edge of the quadrant of altitude to
coincide with the sun's place, then the number of
degrees on the horizon, reckoned from the north or
south point thereof to the graduated edge of the
quadrant, will shew the azimuth ; and the number of de-
grees on the quadrant, counting from the horizon to the
sun's place, will be the sun's altitude.

OR, BY THE ANALEMMA.

Elevate the pole so many degrees above the horizon
as are equal to the latitude of the place, and screw the
quadrant of altitude on the brass meridian, over that
latitude ; bring the middle of the analemma to the brass
meridian, and set the index of the hour-circle to
twelve ; then, if the given time be before noon, turn the
globe eastward on its axis as many hours as it wants of
noon ; but, if the given time be past nown, turn the globe
westward as many hours as it is past noon ; bring the
graduated edge of the quadrant of altitude to coincide
with the day of the month on the analemma, then the
number of degrees on the horizon, reckoned from the
north 01* south point thereof to the graduated edge of the
quadrant, will shew the azimuth; and- the number of
degrees on the quadrant, counting from the horizon to
the day of the month, will be the sun's altitude.

EXAMPLES. 1. What is the sun's altitude, and his
azimuth from the north, at London, on the first of May,
at ten o'clock in the morning ?

Answer. The altitude is 47°, and the azimuth from the north 136°,
or from the south 44°.

2. What is the sun's altitude and azimuth at Peters-
burg on the 13th of August, at half past five o'clock in
the morning ?

3. What is the sun's azimuth and altitude at Antigua,
on the 21st of June, at half past six in the morning, and
at half past ten ? *

* At all places in the torrid zone, whenever the declination of the
sun exceeds the latitude of the place, and both are of the same name,

Chap. I. THE TERRESTRIAL GLOBE. 253

4. At Barbadoes on the 21st of June, required the sun's
azimuth and altitude at 8 minutes past 6, and at f past 9
in the morning: also at £ past 2, and at 52 minutes past 5
in the afternoon.

5. On the 13th of August at half past eight o'clock in
the morning, at sea, in latitude 57° N. the observed azi-
muth of the sun was S. 40° 14' E., what was the sun's
altitude, his true azimuth, and the variation of the com-
pass?

6. On the 14th of January, in latitude 33° 52' S., at
half past three o'clock in the afternoon, the sun's mag-
netic azimuth was observed to be N.630 51' W. ; what
was the true azimuth, the variation of the compass, and
the sun's altitude ?

PROBLEM XLV.

The latitude of the place, day of the month, and the suns
altitude being given, to find the suns azimuth and the
hour of the day.*

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude on the brass meridian,
over that latitude ; bring the sun's place in the ecliptic to
the brass meridian, and set the index of the hour-circle
to twelve ; turn the globe on its axis till the sun's place
in the ecliptic coincides with the given degree of altitude

the sun will appear twice in the forenoon and twice in the afternoon,
on the same point of the compass, and will cause the shadow of an
azimuth dial to go back several degrees. In this example, the sun's
azimuth at the hours given above, will be 69° from the north towards
the east ; and at half past eight o'clock, the sun will appear to have the
same azimuth for some time.

* This problem is only a variation of the preceding ; for, by the
nature of spherical trigonometry, any three of the following quantifies,
viz. the latitude of the place, the suns declination, altitude, azimuth, or
time of the day, being given, the rest may be found, admitting of se-
veral variations. A large collection of Astronomical problems may be
found in Keith's Trigonometry, seventh edit, page 281, &c. These
problems are useful exercises on the globes.

254 PROBLEMS PERFORMED BY Part III.

on the quadrant ; the hours passed over by the index of
the hour-circle will shew the time from noon, and the
azimuth will be found on the horizon, as in the preceding
problem.

OR, BY THE ANALEMMA.

Elevate the pole to the latitude of the place, and screw
the quadrant of altitude over that latitude ; bring the
middle of the analemma to the brass meridian, and set
the index of the hour-circle to twelve ; move the globe
and the quadrant till the day of the month coincides with
the given altitude, the hours passed over by the index will
shew the time from noon, and the azimuth will be found
in the horizon as before.

EXAMPLES. 1. At what hour of the day on the 21st
of March is the sun's altitude 22^° at London, and what
is his azimuth r The observation being made in the after-
noon.

Answer. The time from noon will be found to be 3 hours SO mi-
nutes, and the azimuth 59° 1' from the south towards the west. Had
the observations been made before noon, the time from noon would
have been 3^ hours, viz. it would have been 30 minutes past eight in
the morning, and the azimuth would have been 59° 1' from the south
towards the east.*

2. At what hour on the 9th of March is the sun's alti-
tude 25° at London, and what is his azimuth ? The ob-
servation being made in the forenoon.

3. At what hour on the 18th of May is the sun's alti-
tude 30° at Lisbon, and what is the azimuth ? The observ-
ation being made in the afternoon.

4. Walking along the side of Queen-square in London,
on the 5th of August in the forenoon, I observed the
shadows of the iron-rails to be exactly the same length as
the rails themselves ; pray what o'clock was it, and on
what point of the compass did the shadows of the rails
fall?

* The learner will observe, that the sun has the same altitude at
equal distances from noon ; hence it is necessary to say whether the
observation be made before or after noon, otherwise the problem ad-
mits of two answers.

Chap. I. THE TERRESTRIAL GLOBE. 255

5. In latitude 13°30'N., on the 21st of June, the sun
had the same azimuth at two different times in the morn-
ing ; and also in the afternoon, viz. when his altitude was
7° 17' and 56° 55' ; required the azimuth and the hours of
the day ? It is likewise required to find the azimuth
when it is the greatest, and the hour ; the altitude at that
time being 35° 50'.

PROBLEM XL VI.

Given the latitude of tlie place, and tJie day of the month,
to find at what hour the sun is due east or west.

UULE. Elevate the pole so many degrees above tlie
horizon as are equal to the latitude of the place, find the
sun's place in the ecliptic, bring it to the brass meridian^
and set the index of the hour-circle to twelve ; screw the
quadrant of altitude on the brass meridian, over the
given latitude, and move the lower end of it to the east
point of the horizon ; hold the quadrant in this position,
and move the globe on its axis till the sun's place comes
to the graduated edge of the quadrant ; the hours passed
over by the index from twelve will be the time from noon
when the sun is due east*, and at the same time from
noon he will be due west.

OR, BY THE ANALEMMA.

This is exactly the same as above, only instead of
pringing the sun's place to the meridian, you bring the
analemma there, and, instead of bringing the sun's place
to the graduated edge of the quadrant, the day of the
month on the analemma must be brought to it.

* If the latitude be north, and the sun's declination be south, he
•will be due east and west when he is below the horizon ; and the same
thing will happen if the latitude be south when the declination is north.
Examples exercising these cases are useless ; however they are easily
solved, if we consider that, when the sun is due east below the horizon
at any time, the opposite point of the ecliptic will be due west above
the horizon; therefore, instead of bringing the lower edge of the
quadrant to the east of the horizon, bring it to the west, and, instead
of using the sun's place, make use of a point in the ecliptic diametri-
cal ly opposite.

256 PROBLEMS PERFORMED BY Part III.

EXAMPLES. 1. At what hour will the sun be due
east at London on the 19th of May; at what hour will
he be due west ; and what will his altitude be at these
times ?

Answer. The time from 12, when the sun is due east, is 4 hours
54 minutes ; hence the sun is due east at six minutes past seven
o'clock in the morning, and due west at 54 minutes past four in the
afternoon ; the sun's altitude will be found at the same time, as in
Problem XLIV. In this example it is 25° 26'.

2. At what hours will the sun be due east arid west at
London on the 21st of June, and on the 21st of Decem-
ber ; and what will be his altitude above the horizon on
the 21st of June?

3. Find at what hours the sun will be due east and
west, not only at London, but at every place on the sur-
face of the globe, on the 21st of March and on the 23d of
September ?

4. At what hours is the sun due east and west at
Buenos Ayres on the 21st of December'?.

PROBLEM XL VII.

Given the, suns meridian altitude, and the day of the month,
to find the latitude of the place.

RULE. Find the sun's place in the ecliptic, and bring
it to that part of the brass meridian which is numbered
from the equator towards the poles ; then, if the sun
was south * of the observer when the altitude was taken,
count the number of degrees from the sun's place on the
brass meridian towards the south point of the horizon,
and mark where the reckoning ends ; bring this mark to
coincide with the south point of the horizon, and the
elevation of the north pole will shew the latitude. If
the sun was north of the observer when the altitude
was taken, the degrees must be counted in a similar
manner, from the sun's place towards the north point

* It is necessary to state whether the sun be to the north or south of
the observer at noon, otherwise the prpblem is unlimited.

Chop. 1. THE TERRESTRIAL GLOBE. 257

of the horizon, and the elevation of the south pole will
shew the latitude.

OR. WITHOUT A GLOBE.

Subtract the sun's altitude from ninety degrees, the
remainder is the zenith distance. If the sun be south
when his altitude is taken, call the zenith distance north ;
but, if north, call it south ; find the sun's declination in
an ephemeris * or a table of the sun's declination, and
mark whether it be north or south ; then, if the zenith
distance, and declination have the same name, their sum
is the latitude, but, if they have contrary names, their
difference is the latitude, and it is always of the same
name with the greater of the two quantities.

EXAMPLES. On the 10th of May 1842, I observed
the sun's meridian altitude to be 50°, and it was south of
me at that time ;• required the latitude of the place ?

Answer. 57° 35' north.

By calculation.
90° 0'
50 0 S., sun's altitude at noon.

40 0 JV., the zenith's distance.

17 35 N., the sun's declination 10th May 1842.

57 35 N., the latitude sought.

2. On the 10th of May 1842, the sun's meridian alti-
tude was observed to be 50°, and it was north of the ob-
server at that time ; required the latitude of the place ?

Answer. 22° 25' south.

J$ij calculation*
99° 0'
50 0 N., sun's altitude at noon.

40 OS., the zenith's distance.

17 35 N., the sun's declination 10th May 1842.

22 25 S., the latitude sought.

• The most convenient is the Nautical Almanac, or White's Ephe-
meris ; see the note page 41.

258 PROBLEMS PERFORMED BY Part III.

3. On the 5tb of August 184-2, the sun's meridian alti-
tude was observed to be 74° 30' north of the observer ;
what was the latitude ?

4. On the 19th of November 1842, the sun's meridian
altitude was observed to be 40° south of the observer;
what was the latitude ?

5. At a certain place, where the clocks are two hours
faster than at London, the sun's meridian altitude was
observed to be 30 degrees to the south of the observer
on the 21st of March ; required the place ?

6. At a place where the clocks are five hours slower
than at London, the sun's meridian altitude was observed
to be 60° to the south of the observer on the 16th of
April 1843 ; required the place?

PROBLEM XLVIIL

The length of the longest day at any place, not within tJie
polar circles, being given, to find the latitude of that
place.

RULE. Bring the first point of Cancer or Capricorn to
the brass meridian (according as the place is on the
north or south side of the equator), and set the index o£
the hour-circle to twelve ; turn the globe westward on its
axis till the index of the hour circle has passed over as
many hours as are equal to half the length of the day ;
elevate or depress the pole till the sun's place (viz. Can-
cer or Capricorn) comes to the horizon ; then the elev-
ation of the pole will shew the latitude.

NOTE. This problem will answer for any day in the year, as well
as the longest day, by bringing the sun's place to the brass meridian
and proceeding as above.

OR, Bring the middle of the analemma to the brass meridian, and
set the index of the hour-circle to 1 2 ; turn the globe westward on its
axis till the index has passed over as many hours as are equal to half
the length of the day ; elevate or depress the pole till the day of the
month coincides with the horizon, then the elevation of the pole will
shew the latitude.

EXAMPLES. 1. In what degree of north latitude, and
at what places is the length of the longest day 1 6| hours ?

Chap. I. THE TERRESTRIAL GLOBE. 259

Answer. In latitude 52°, and all places situated on, or near that
parallel of latitude, have the same length of the day.

2. In what degree of south latitude, and at what places
is the longest day 14 hours?

3. In what degree of north latitude is the length of the
longest day three times the length of the shortest night ?

4. There is a town in Norway where the longest day is
five times the length of the shortest night ; pray what is
the name of the town ?

5. In what latitude north does the sun set at seven
o'clock on the 5th of April ?

6. In what latitude south does the sun rise at five
o'clock on the 25th of November ?

7. In what latitude north is the 20th of May 16 hours
long?

8. In what latitude north is the night of the 15th of
August 10 hours long ?

PROBLEM XLIX.

The latitude of a place and the day of the month being given,
to find how much the suns declination must vary to make
the day an hour longer or shorter than the given day.

RULE. Find the sun's declination for the given day,
and elevate the pole to that declination ; bring the given
place to the brass meridian, and set the index of the hour-
circle to twelve : turn the globe eastward on its axis till
the given place comes to the horizon, and observe the
hours passed over by the index. Then, if the days be in-
creasing, continue the motion of the globe eastward till
the index has passed over another half hour, and raise or
depress the pole till the place comes again into the hori-
zon, the elevation of the pole will shew the sun's declin-
ation when the day is an hour longer than the given day ;
but, if the days be decreasing, after the place is brought
to the eastern part of the horizon, turn the globe westward
till the index has passed over half an hour, then raise or
depress the pole till the place comes a second time into
the horizon, the last elevation of the pole will shew the
sun's declination when the day is an hour shorter than
the given day.

260 PROBLEMS PERFORMED BY Part III.

OR,

Elevate the pole to the latitude of the place, find
the sun's place in the ecliptic, bring it to the brass
meridian, and set the index of the hour-circle to twelve ;
turn the globe westward on its axis till the sun's place
comes to the horizon, and observe the hours passed
over by the index ; then, if the days be increasing, con-
tinue the motion of the globe westward till the index has
passed over another half hour, and observe what point
.of the ecliptic is cut by the horizon ; that point will shew
the sun's place when the day is an hour longer than the
given day, whence the declination is readily found : but,
if the days be decreasing, turn the globe eastward till
the index has passed over half an hour, and observe what
point of the ecliptic is cut by the horizon ; that point
will shew the sun's place when the day is an hour shorter
than the given day.

OR, BY THE ANALEMMA.

Proceed exactly the same as above, only, instead of
bringing the sun's place to the brass meridian, bring the
analemma there, and instead of the sun's place, use the
day of the month on the analemma.

EXAMPLES. 1. How much must the sun's declination
vary that the day at London may be increased one hour
from the 24th of February ?

Answer. On the 24th of February the sun's declination is 9° 38'
south, and the sun sets at a quarter past five ; when the sun sets at
three quarters past five, his declination will be found to be about 4^-°
south, answering to the tenth of March : hence the declination has
decreased 5° 23', and the days have increased 1 hour in 14 days.

2. How much must the sun's declination vary that the
day at London may decrease one hour in length from the
26th of July?

Answer. The sun's declination on the 26th of July is 19° 38' north,
and the sun sets at 49 min. past seven ; when the sun sets at 1 9 min.
past seven, his declination will be found to be 14° 43' north, answer-
ing to the 13th of August : hence the declination has decreased 5° 55',
and the days have decreased one hour in 18 days.

3. How much must the sun's declination vary from the
5th of April, that the day at Petersburg may increase
one hour ?

Chap. I. THE TERRESTRIAL GLOBE. 261

4. How much must the sun's declination vary, from the
4th of October, that the day at Stockholm may decrease
one hour ?

5. What is the difference in the sun's declination, when
he rises at seven o'clock at Petersburg, and when he sets
at nine ?

PROBLEM L.

To find the suns riyht ascension, oblique ascension, oblique
descension, ascensional difference, and time of rising and
setting at any place.

RULE.- Find the sun's place in the ecliptic, and bring
it to that part of the brass meridian which is numbered
from the equator towards the poles * ; the degree on the
equator cut by the graduated edge of the brass meridian,
reckoning from the point Aries eastward, will be the sun's
right ascension.

Elevate the poles so many degrees above the horizon
as are equal to the latitude of the place, bring the sun's
place in the ecliptic to the eastern part of the horizon f ,
and the degree on the equator cut by the horizon,
reckoning from the point Aries eastward, will be the
sun's oblique ascension. Bring the sun's place in the
ecliptic to the western part of the horizon J, and the degree
on the equator cut by the horizon, reckoning from the point
Aries eastward, will be the sun's oblique descension.

Find the difference between the sun's right and oblique
ascension ; or, which is the same thing, the difference
between the right ascension and oblique descension, and
turn this difference into time by multiplying by 4 § :
then, if the sun's declination and the latitude of the place
be both of the same name, viz. both north or both south,
the sun rises before six and sets after six, by a space of
time equal to the ascensional difference ; but if the sun's

* The degree on the meridian above the sun's place is the sun's de«
clination. See Prob. XX.

t The rising amplitude may be seen at the same time. See Pro-
blem XLIII.

J The setting amplitude may here be seen. Vide Prob. XLIII*

§ See Problem XVIII.

PROBLEMS PERFORMED BY Part III.

declination and the latitude be of contrary names, viz. the
one north and the other south, the sun rises after six and
sets before six.

EXAMPLES. ] . Required the sun's right ascension, ob-
lique ascension, oblique descension, ascensional difference,
and time of rising and setting at London, on the 15th of
April ?

Ansiuer. The right ascension is 23° 30^ the oblique ascension is
90 45' the ascensional difference (23° 30'— 9° 45' =) 13° 45', or
55 minutes of time ; consequently the sun rises 55 minutes before 6,
or 5 min. past 5, and sets 55 mm. past 6. The oblique descension is
37° 15'; consequently the descensional difference is (37° 15'-—
23° 30' =) 13° 45', the same as the ascensional difference:

2. What are the sun's right ascension, oblique ascen-
sion, and oblique descension, on the 27th of October at
London ; what is the ascensional difference, and at what
time does the sun rise and set ?

3. What are the sun's right ascension, declination,
oblique ascension, rising amplitude, oblique descension,
and setting amplitude at London, on the 1st of May;
what is the ascensional difference, and at what time does
the sun rise and set ?

4. What are the sun's right ascension, declination,
oblique ascension, rising amplitude, oblique descension,
and setting amplitude, at Petersburg, on the 21st of June;
what is the ascensional difference, and what time does the
sun rise and set ?

5. What are the sun's right ascension, declination,
oblique ascension, rising amplitude, oblique descension,
and setting amplitude, at Alexandria, on the 21st of De-
cember; what is the ascensional difference, and what
time does the sun rise and set ?

PROBLEM LI.

Given the day of the month and the suns amplitude, to find
the latitude of the place of observation.

RULE. Find the sun's place in the ecliptic, and bring
it to the eastern or western part of the horizon (according
as the eastern or western amplitude is given) ; elevate or

Chap. I. THE TERRESTRIAL GLOBE. 263

depress the pole till the sun's place coincides with the
given amplitude on the horizon, then l^ie elevation of the
pole will show the latitude.

OR, THUS :

Elevate the north pole to the complement* of the
amplitude, and screw the quadrant of altitude upon the
brass meridian over the same degree : bring the equi-
noctial point Aries to the brass meridian, and move the
quadrant of altitude till the sun's declination for the
given day (counted on the quadrant) coincides with
the equator ; the number of degrees between the point
Aries and the graduated edge of the quadrant will be
the latitude sought.

EXAMPLES. 1. The sun's amplitude was observed to
be 39° 48' from the east towards the north, on the 21st
of June ; required the latitude qf the place ?

Answer. 51° 32' north.f

2. The sun's amplitude was observed to be 15° 3(X
from the east towards the north, at the same time his
declination was 15° 30' ; required the latitude ?

3. On the 29th of May, when the sun's declination
was 21° 30' north, his rising amplitude was known to
be 22° northward of the east ; required the latitude ?

4. When the sun's declination was 2° north, his rising
amplitude was 4° north of the east ; required the latitude?

PROBLEM LII.

Given two observed altitudes of the sun, the time elapsed
between them, and the suns declination, to find the
latitude.

RULE. Take a number of degrees equal to the sun's
decimation from the equator with a pair of compasses, and

* The complement of the amplitude is found by subtracting the
amplitude from 90°. This rule is exactly the same as above ; for it is
formed from a right-angled spherical triangle, the base being the com-
plement of the amplitude, the perpendicular the latitude of .the place,
and the hypothenuse the complement of the sun's declination.

t See Keith's Trigonometry, fourth edition, page 285.

264 PROBLEMS PERFORMED BY Part III.

apply the same number of degrees upon the meridian
passing through Libra* from the equator northward or
southward, and mark where they extend to ; turn the
elapsed time into degrees-}-, and count those degrees
upon the equator from the meridian passing through
Libra ; bring that point of the equator where the
reckoning ends to the graduated edge of the brass
meridian, and set off the sun's declination from that point
along the edge of the meridian, the same way as before ;
then take the complement of the first altitude from
the equator in your compasses, and with one foot in
the sun's declination, and a fine pencil in the other
foot, describe an arc ; take the complement of the second
altitude in a similar manner from the equator, and with
one foot of the compasses fixed in the second point of
the sun's declination, cross the former arc : the point of
intersection brought to that part of the brass meridian
which is numbered from the equator towards the poles,
will stand under the degree of latitude sought.

EXAMPLES. 1. Suppose on the 4th of June, 1839.
in north latitude, the sun's altitude at 29 minutes past
10 in the forenoon, to be 65° 24', and at 31 minutes
past 12, 74° 8' : required the latitude ?

Answer. The sun's declination is 22° 22' north, the elapsed time
two hours two min. answering to 30° 30'; the complement of the first
altitude 24° 36f, the complement of the second altitude 15° 52', and
the latitude sought 36° 57' north.

2. J Given the sun's declination 19° 39' north* his
altitude in the forenoon 38° 19', and, at the end of one
hour and a half, the same morning, the altitude was
50° 25' ; required the latitude of the place, supposing
it to be north ?

3. When the sun's declination was 22° 40' north, his

* Any meridian will answer the purpose as well as that which
passes through Libra; on Adams' and on Caiy's globes this meridian
is divided like the brass meridian. If Newton's globes be used take
the meridian passing through Cancer.

•f- See the method of turning time into degrees. Prob. XIX.

$ A great variety of examples accurately calculated by a general
rule, without an assumed latitude, may be seen in Keith's Trigono-
metry : seventh edition, page 323, &c.

Chap. I. THE TERRESTRIAL GLOBE. 265

altitude at 10 h. 54 m. in the forenoon was 53° 29', and
at 1 h. 17m. in the afternoon it was 52° 48'; required the
latitude of the place of observation, supposing it to be
north ?

4. In north latitude, when the sun's declination was
22° 23' south, the sun's altitude in the afternoon was
observed to be 14° 46', and after 1 h. 22 m. had elapsed,
his altitude was 8° 27' ; required the latitude ?

PROBLEM LIU.

The day and hour being given when a solar * eclipse will
happen, to find where it will be visible.

RULE. Find the sun's declination, and elevate the
pole agreeably to that declination ; bring the place at
which the hour is given to that part of the brass meri-
dian which is numbered from the equator towards the
poles, and set the index of the hour-circle to twelve ;
then, if the given time be before noon, turn the globe
•westward till the index has passed over as many hours as
the given time wants of noon ; if the time be past noon,
turn the globe eastward as many hours as it is past noon,
and exactly under the degree of the sun's declination on
the brass meridian you will find the place on the globe
where the sun will be vertically eclipsed t: at all places
within 70 degrees of this place, the eclipse may\. be
visible, especially if it be a total eclipse.

EXAMPLE. On the 9th of October, 1847, at 29 min.
past seven o'clock in the morning at London, there

* The term Solar Eclipse is continued conformably to general
usage; but see note, page 174. — ED.

f The effect of parallax is so great, that an eclipse may not be
visible even where the sun is vertical.

$ When the moon is exactly in the node, and when the axes of the
moon's shadow and penumbra pass through the centre of the earth, the
breadth of the earth's surface under the penumbral shadow is 70° 20':
but the breadth of this shadow is variable ; and if it be not accurately
determined by calculation, it is impossible to tell by the globe to what
extent an eclipse of the sun will be visible.
N

266 PROBLEMS PERFORMED BY Part III.

will be an eclipse of the sun, where will it be visible,
supposing the moon's penumbral shadow should extend
northward 70 degrees from the place where the sun will
be vertically eclipsed ?.

Answer.- To the whole of Arabia, Persia, Hindoostan, &c. For
more examples consult the Table of Eclipses following the next problem.

PROBLEM LIV.

The day and hour being given when a lunar eclipse will
happen, to find where it will be visible.

RULE. Find the sun's declination for the given day,
and note whether it be north or south ; if it be north,
elevate the south pole so many degrees above the horizon
as are equal to the declination ; if it be south, elevate the
north pole in a similar manner ; bring the place at which
the hour is given to that part of the brass meridian which
is numbered from the equator towards the poles, and set
the index of the hour-circle to twelve ; then, if the given
time be before noon, turn the globe westward as many
hours as it wants of noon ; if after noon, turn the globe
eastward as many hours as it is past noon ; the place
exactly under the degree of the sun's declination will be
the antipodes of the place where the moon is vertically
eclipsed ; set the index of the hour-circle again to twelve,
and turn the globe on its axis till the index has passed
over twelve hours ; then to all places above the horizon
the eclipse will be visible; to those places along the
western edge of the horizon the moon will rise eclipsed ;
to those along the eastern edge she will set eclipsed ; and
to that place immediately under the degree of the sun's
declination, reckoned towards the elevated pole, the moon
will be vertically eclipsed.

EXAMPLE. On the 31st of May, 1844, at 50 minutes
past ten in the evening at London, there will be an eclipse
of the moon ; where will it be visible ?

Answer. It will be visible to the whole of Europe, Africa, and the
greater part of the continent of Asia. For more examples see the
following Table of Eclipses, and pages 271. and 272.

NOTE. The substance of the following Table of Eclipses was ex-
tracted from Dr. Hutton's translation of Montucla's edition of Ozanam's
Mathematical and Physical Recreations, published by Mr. Kearsley in

Chap. I. THE TERRESTRIAL GLOBE.

267

Fleet-street. These eclipses were originally calculated by M. Pin-
gre, a member of the Academy of Sciences, and published in L' Art
de verifier les Dates. In classing these tables the arrangement of
Mr. Ferguson has been followed; see page 267 of his Astronomy,
where a catalogue of the visible eclipses is given from 1700 to 1800,
taken from L'Art de verifier les Dates. It may be necessary to inform
the learner, that the times of these eclipses, as calculated by M. Pingre,
are not perfectly accurate, and were only designed to shew nearly the
time when an eclipse may be expected to happen. The limits where
these eclipses are visible are generally from the tropic of Cancer in
Africa, to the northern extremity of Lapland, and from the 5th degree
of north latitude in Asia, to the north polar circle ; though some few
of them are visible beyond the pole. In longitude, the limits are the
fifth and 1 55th meridians, supposing the 20th to pass through Paris :
hence it appears that they are calculated for the meridian of Ferro ;
which will make their limits from London to be from 12° 46' west
long, to 1 37° 1 4' east. M. Pingr6 says, that an eclipse of the sun is
visible from 32° to 64° north, and as far south of the place where it is
central. In the following table the moon is represented by ]) , the
sun by ©, T stands for total, P for partial, M for morning, and A
for afternoon, the rest is obvious.

Months
and
Days.

Time.

Months
and
Days.

Time.

1823

HI
1824-

>T
O

D P
©

D P
j) T
D T
0

fp
D P
9

Jan. 26
Feb. 11
July 8
July 23
Jan. 16
June 26
July 11
Dec. 20
June 1
June 16
Nov. 25
May 21
Nov. 14
Nov. 29
April 26
May 11
Nov. 3
April 14

5^ A
3 M
6±M
?£M
9 M
Hi A
44 M
11 M
0£M
0£ A
4i A
3£ A
4£ A
11£M
3^M
8|M
5 A
9f M

1828
1829

D P
» P
©

D P
D P

J> T

•j?

D P

Oct. 9
March 20
Sept. 13
Sept. 28
Feb. 23
March 9
Sept. 2
Feb. 26
Aug. 23
July 27
Jan. 6
July 2
July 17
Dec. 26
June 21
Dec. 16
May 27
June 10

Oi M
2 A
7 M
2A M
5 M
2 A
11 A
5 A
10* M
2i A
8 M
1 M
7 M
10 A
8J M.
5£ M
4 A
11 A

1830

1831

1825

1832
1833

1826
1827

1834

1835

1828

N 2

268

PROBLEMS PERFORMED BY

Part III.

£
5

Months
and
Days.

Time.

£'

Months
and
Days.

Time.

1835
1836

0
D P

D P

?F
I?

0
0

ii
?p

IT
} P

0
0

£P

|JT

Nov. 20.
May 1
May 15
Oct. 24
April 20
May 4
Oct. 13
April 10
Oct. 3
March 15
Sept. 7
Feb. 17
March 4
Aug. 13
Feb. 6
Feb. 21
July 18
Aug. 2
Jan. 26
JulyS
July 22
June 12
Dec. 7
Dec. 21
May 31
Nov. 25
May 6
May 21
Nov. 14
April 25
Oct. 20
March 31
Sept. 24
Oct. 9
March 19
ISept. 13

11 M

84 M
24 A
1| A
9 A
74 A
114 A
2^ M
3 A
2£ A
lol A
2 A
4 M
74 M
2J M
11 M
2 A
10 M
6 A
7 M
11 M
8 M
0£ M
54 M
11 A
Oi M
8£ M
43 A
1 M
5i A
8* M
9l A
3 A

n\ M

9i A
6i M

1848
1849

0
0

D P
D P
0

fp
j'

?TP

0
D T
D P
0
D P
0
D P
0
D P
D T

?T
D P

0
J> P

0
0

Sept. 27
Feb. 23
March 9
Sept. 2
Feb. 12
Aug. 7
Jan. 17
July 13
July 28
Jan. 7
July 1
Dec. 11
Dec. 26
June 21
May 12
Nov. 4
May 2
May 16
Oct. 25
April 20
Sept. 29
Oct. 13
Sept. 18
Feb. 27
March 15
Aug. 24
Feb. 17
July 29
Aug. 13
Feb. 7
July 18
Aug. 1
Jan. 11
July8
Dec. 17
Dec. 31

10 M

14 M
1 M
54 A
-64 M
10 A
5 A
74 M
24 A
64 M
3J A
4 M
1 A
6 M
4 A
94 A
4J M
24 M
8 M
94 M
4 M
114 A
6 M
10J A
0* A
24 A
11 M
94 A
4£ A
24 M
2 A
54 A
34 M
2 M
84 M
24 A

1850

1837

1851

1838

1839

1852

1840

1853
1854

1841

1855

184-2

1856

1843

1857
1858

1844

1845

1859

1846

1860

J1847
11848

1861

THE TERRESTRIAL GLOBE.

269

Months
and
Days.

Time.

»H

Months
and
Days.

Time.

1862

D T

D T
D P

0
D P
D P

0
0
j) T

D T
0
0

D P
D P
0

0
J) P

D P
0

D T
D T

J> P
0
D P
0
D P
D T

)> T
» P

June 12
Dec. 6
Dec. 21
May 17
June 2
Nov. 25
May 6
April 11
Oct. 4
Oct. 19
March 16
Marrh 31

6JM
8 M
5| M
5 A
0 M
9 M
OJM
5 M
11 A
5 A
10 A
5 M
21 A
5£ A
10 M
9 M
1 M
2i A
5£M
1JM
2 A
10 A
3 A
11 A
Of A
9i A
2^M
li A
4iM
Hi A
3iM
5|M
HiM
9iM
4i A
4i A

1874-

D P

D P
D T

0
0
j) T

D P
0
D P
0
0
D P

0
0

» T
D P

D P
0

D P
D P
0
D P

Oct. 10
Oct. 25
April 6
Sept. 29
March 10
Sept. 3
Feb. 27
March 15
Aug. 9
Aug. 23
Feb. 17
July 29
Aug. 13
Jan. 22
July 19
Dec. 28
Jan. 11
June 22
Dec. 16
Dec. 31
May 28
June 12
Dec. 5
May 17
Nov. 11
April 22
Oct. 16
Oct. 31
March 27
April 10
Oct. 4
Oct. 19
March 30
Sept. 24
Aug. 29
Feb. 8

Hi M

8 M

7 M
li A
6i M
9* A
7i A
3 M
5 M
Hi A
Hi M
9i A
Oi M
Merid.
9 M
4i A
11 A
2 A
4 A
2 A
0 M
7i M
5i A
8 M
0 M
Merid.
7i M
Oi M
6 M
Merid.
10i A
1 M
5 A
8 j M

ii A

10i M

1863

1864-
1865

1866

1875

1876

1877

1878

Sept. 24
Oct. 8
March 6
TVTarrh Of)

1879

1867

1868
1869

Sept. 14?
Feb. 23
Aug. 18
Jan. 28
July 23
Aug. 7
Jan. 17
July 12
Dec. 22
Jan. 6
June 18
July 2
Dec. 12
May 22
June 6
Nov. 15
May 12
May 26
Nov. 4
May 1

1880

1881

;1870

1882

1871

1883

1872
1873

1884

1885

1886
1887

1874

270

PROBLEMS PERFORMED BY

Part III.

K*^

Months
and
Days.

Time.

?*i

Months
and
Days.

Time.

1887

D P

D P
D P

D P

D T
D P
D T
0
D P
0
D P

Aug. 3
Aug. 19
Jan. 28
July 23
Jan. 17
July 12
Dec. 22
June 23
June 17
Nov. 26
May 23
June 6
Nov. 16
May 11
Nov. 4?
April 16
March 21
April 6
Sept. 15
Sept. 29

9 A
6 M
1H A
6" M
5J M
9 A
1 A
6 M
10 M
2 A
7 A
4£ A
OJ M
111 A
4fc A
3 A
21 A
4* M
4} M
Si M

1895

D 1
0

>I
j> p

No
D P
0
D P
» T
0

D P
0

March 1 1
March 26
Aug. 20
Sept. 4
Feb. 28
Aug. 9
Aug. 23
visible EC
Jan. 8
Jan. 22
July 3
Dec. 27
Jan, 11
June 8
June 23
Dec. 17
May 28
June 13
Nov. 22

4 M
10 M
0£ A
6 M
8 A
41 M
7 M
;lipse.
Oi M
8 M
9k A
12 A
11 A
7 M
2£ A
1* M
3J A
4 M
8 M

1888
1889

1896

1890!

1897
1898

;

1891J

1892

1899

1893
1894

1900

PROBLEM LV.

To find the time of the year when the Sun and Moon will
be liable to be eclipsed.

RULE 1. Find the place of the moon's nodes, the time
of new moon, and the sun's longitude at that time, by an
epheineris, as the Nautical Almanac ; then if the sun be
within 17 degrees of the moon's node, there will be an
eclipse of the sun.

2. Find the place of the moon's nodes, the time of full
moon, and the sun's longitude at that time, by an ephe-
meris : then, if the sun's longitude be in opposition to that
of the moon, and the moon's longitude be within 12
degrees of her node, there will be an eclipse of the moon.

Chap. I. THE TERRESTRIAL GLOBE. 271

OR, WITHOUT THE EPHEMERIS.

The mean annual variation of the moon's node, which
is retrograde, is 19° 19'-?, or more nearly 19° 19X 42"-316,
and the daily motion 3'-18, the place of the ascending
node for the first of January, 1840, being 339° 36'*4, its
place for any other time may therefore be found.

For example, on the 1st of January 1841, the d's ascending node
was, according to the rule, 320° 16' -7, viz. 339° 36' -4 — 19° 19^7 ;
but because 1840 was leap year and consisted of 366 days, 3' -18 must
be deducted, for the extra day, from 320° 16' -7 making 320° 13''5,
the same as given in the Nautical Almanac, p. 266.

On the 1st of Jan. 1845 the j) 's ascending node will be 339° 36' -4.
minus 5 times 19° 19' '7, together with twice 3/-18 for leap years, in
1840 and 1844, making 339° 36' '4 — 96° 44' -9 =242° 51 ''5, the j) '«
ascending node, the descending node being opposite to it must be
242° 51'-5 - 180° = 62° 51'-5.

The time of new moon may be found as directed at
page 1 85., and the sun's longitude is the sun's place in the
ecliptic.* The rest may be found as above.

EXAMPLES. 1. On the 31st of May, 1844, there will
be a full moon, at which time the place of the moon's as-
cending node will be 254° 14', and her longitude 250° or
10° in f , and the sun's longitude ?]° ; will an eclipse of
the moon happen at that time ?

Answer. Here the sun's longitude being in opposition to that of
the moon's, and the moon's longitude within 1 2 degrees of the moon's
node, there will be an eclipse of the moon. — When the moon is in
one of her nodes at the time of full moon, the sun is in the other
node, and the earth is directly between them.

2. There was a new moon on the 8th of July, 1842, at
which time the place of the moon's ascending node was
290° 43^, and opposite node 110° 43', her longitude was
105° 36', and the sun's longitude 106° 55'; was there an
eclipse of the sun at that time ?

3. There will be a full moon on the 6th of December,
1843, at which time the place of the moon's node will be
263° 34', and her longitude 74°, the sun's longitude
254° 16'; will there be an eclipse of the moon at that
time?

* The moon's longitude maybe found thus: Multiply 12° 11'
26//44 by the moon's age (see p. 184.), the product will give the num-
ber of degrees by which the moon's longitude exceeds that of the sun.

272 PROBLEMS PERFORMED BY Part III.

4. On the 24th of November, 181-4, there will be a full
moon, at which time the place of the moon's node will be
244° 39', her opposite node 64° 39', and longitude 62^°,
and the sun's longitude 242° 22' ; will there be an eclipse
of the moon on that day ?

5. On the 30th of October, 1845, there will be a new
moon, at which time the place of the moon's ascending
node will be 226° 51', her longitude at noon 224° 37', and
latitude 0° 11' S., and the sun's longitude will be 217° 57',
lat. 0° ; will there be an eclipse of the sun on that day ?

PROBLEM LVI.
To explain the phenomenon of the harvest moon.

DEFINITION 1. The harvest moon, in north latitude, is
the full moon which happens at, or near, the time of the
autumnal equinox; for, to the inhabitants of north latitude,
whenever the moon is in Pisces or Aries (and she is in
these signs twelve times in a year), there is very little dif-
ference between her times of rising for several nights toge-
ther, because her orbit is at these times nearly parallel to
the horizon. This peculiar rising of the moon passes unob-
served at all other times of the year except in September
and October ; for there never can be a full moon except
the sun be directly opposite to the moon ; and as this par-
ticular rising of the moon can only happen when the moon
is in K Pisces or <Y* Aries, the sun must necessarily be
either in tfR Virgo or =^= Libra at that time, and these
signs answer to the months of September and October.

DEFINITION 2. The harvest moon, in south latitude, is
the full moon which happens at, or near, the time of the
vernal equinox ; for, to the inhabitants of south latitude,
whenever the moon is in rrg Virgo or ^= Libra (and she is
in these signs twelve times in a year), her orbit is nearly
parallel to the horizon : but when the full moon happens
in tJ£ Virgo or =ct Libra, the sun must be either in X Pisces
or <y> Aries. Hence it appears that the harvest moons are
just as regular in south latitude as they are in north lati-
tude, only they happen at contrary times of the year.

Chap. I. THE TERRESTRIAL GLOBE 273

RULE FOR PERFORMING THE PROBLEM 1. For north

latitude. Elevate the north pole to the latitude of
the place, put a patch or make a mark in the ecliptic
on the point Aries, and upon every twelve* degrees
preceding and following that point, till there be ten
or eleven marks; bring that mark which is the nearest
to Pisces to the eastern edge of the horizon, and set
the index to 12; turn the globe westward till the
other marks successively come to the horizon, and ob-
serve the hours passed over by the index ; the intervals
of time between the marks coming to the horizon will
shew the diurnal difference of time between the moon's
rising. If these marks be brought to the western edge
of the horizon in the same manner, you will see the
diurnal difference of time between the moon's setting:
for, when there is the smallest difference between the
times of the moon's rising f, there will be the greatest
difference between the times of her setting; and, on
the contrary, when there is the greatest difference be-
tween the times of the moon's rising, there will be
the least difference between the times of her setting.

NOTE. As the moon's nodes vary their position and form a com-
plete revolution in about nineteen years, there will be a regular period
of all the varieties which can happen in the rising and setting of the
moon during that time. The following table (extracted from Fergu-
son's Astronomy) shews in what years the harvest moons are the least
and most beneficial, with regard to the times of their rising, from 1 823
to 1 860. The columns of years under the letter L are those in which
the harvest moons are least beneficial, because they fall about the do-
scending node ; and those under M are the most beneficial, because
they fall about the ascending node.

* The reason why you mark every 1 2 degrees is, that the moon
gains 12° 1 1'SCM" of the sun in the ecliptic every day (see the 2d note,
p. 8'J. and 83).

t At London, when the moon rises in the point Aries, the ecliptic
at that point makes an angle of only 15 degrees with the horizon;
but when she sets in the point Aries, it makes an angle of 62 degrees :
and, when the moon rises in the point Libra, the ecliptic, at that point,
makes an angle of 62 degrees with the horizon ; but, when she sets
in the point Libra, it only makes an angle of 15 degrees with the
horizon.

N 5

274- PROBLEMS PERFORMED BY Part III.

L L L L

1826 1831 1845 1849

1827 1832 1846 1850

1828 1833 1847 1851

1829 1834 1848 1852

1830 1844

M M M M

1823 1837 1842 1856

1824 1838 1843 1857

1825 1839 1853 1858

1835 1840 1854 1859

1836 1841 1855 1860

2. For south latitude. Elevate the south pole to the
latitude of the place, put a patch or make a mark on the
ecliptic on the point Libra, arid upon every twelve
degrees preceding and following that point, till there
be ten or eleven marks ; bring that mark which is the
nearest to Virgo, to the eastern edge of the horizon,
and set the index to 12 ; turn the globe westward till the
other marks successively come to the horizon, and observe
the hours passed over by the index; the intervals of
time between the marks coming to the horizon will be
the diurnal difference of time between the moon's rising,
&c. as in the foregoing part of the problem. *

PROBLEM LVI1.

The day and hour of an eclipse of any one of the satellites
of Jupiter being given, to find upon the globe all those
places where it will be visible.

RULE. Find the sun's declination for the given day,
and elevate the pole to that declination ; bring the place
at which the hour is given to the brass meridian, and set
the index of the hour circle to 12 ; then, if the given time
be before noon, turn the globe westward as many hours
as it wants of noon ; if after noon, turn the globe eastward
as many hours as it is past noon ; fix the globe in this
position : THEN,

* This solution is on a supposition that the moon keeps constantly
in the ecliptic, which is sufficiently accurate for illustrating the pro-
blem. Otherwise the latitude and longitude of the moon, or her right
ascension and declination, may be taken from the Ephemeris, at the
time of full moon, and a few days preceding and following it ; her
place will be then truly marked on the globe.

Chap. I. THE TERRESTRIAL GLOBE. 275

1. If Jupiter rise after the sun*, that is, if he be an
evening star, draw a line along the eastern edge of the
horizon with a black lead pencil, this line will pass over
all places on the earth where the sun is setting at the
given hour ; turn the globe westward on its axis till as
many degrees of the equator have passed under the brass
meridian as are equal to the difference between the sun's
and Jupiter's right ascension ; keep the globe from re-
volving on its axis, and elevate the pole as many degrees
above the horizon as are equal to Jupiter's declination,
then draw another line with a pencil along the eastern
edge of the horizon : the eclipse will be visible to every
place between these lines, viz. from the time of the sun's
setting to the time of Jupiter's setting.

2. If Jupiter rise before the sun\, that is, if he be a
morning star, draw a line along the western edge of the
horizon with a black lead pencil, this line will pass over
all places of the earth where the sun is rising at the given
hour ; turn the globe eastward on its axis till as many
degrees of the equator have passed under the brass me-
ridian as are equal to the difference between the sun's
and Jupiter's right ascension ; keep the globe from re-
volving on its axis, and elevate the pole as many degrees
above the horizon as are equal to Jupiter's declination,
then draw another line with a pencil along the western
edge of the horizon : the eclipse will be visible to every
place between these lines, viz. from the time of Jupiter's
rising to the time of the sun's rising.

EXAMPLES. 1. On the 27th of August, 1845, there
will be an immersion of the first satellite of Jupiter at
21 m. 18 sec. past eleven o'clock in the evening at Green-
wich ; where will it be visible ? Jupiter's right ascension
at that time will be 2 hrs. 35 m., and longitude 41° 10',
and his declination 13° 48' N., the sun's right ascension
10 hrs. 24 m., and longitude 152° 5'.

Answer. In this example the longitude of the suu exceeds the
longitude of Jupiter, therefore Jupiter will be to the west of the sun

* Jupiter rises and sets after the sun, and is an evening star unless
too near the sun, when he is to the east of the sun; his longitude at
that time being generally greater than the sun's longitude.

f Jupiter rises before the sun, and is a morning star when he is
west of the sun; his longitude at that time being generally less than
the sun's longitude.

276 PROBLEMS PERFORMED BY Part 111.

and be a morning star, but will also, owing to his position, be seen
late in the evening.

If Jupiter's longitude in the ecliptic be brought to the brass meri-
dian, his place will stand under the degree of his declination * ; and
his right ascension will be found on the equator, reckoning from
Aries. This eclipse will be visible at Greenwich to the whole of
Europe, the greater part of Africa, Madagascar, Persia, Hindoostan, &c.

2. On the 21st of September, 184-3, at 44 min. past
eight o'clock in the evening, at Greenwich, there will be
an emersion of the first satellite of Jupiter ; where will
the eclipse be visible ? Jupiter's right ascension will be
21 h. 25 m. at that time, and longitude about 10 signs
19° 10', and his declination 16° 23' south.

3. On the 18th of November, 1844, at 14 m. 25 sec. past
seven o'clock in the evening, at Greenwich, there will be
an emersion of the first satellite of Jupiter ; where will it
be visible ? Jupiter's right ascension at that time will be
23 h. 41m., and longitude about 11 signs 25° 11', and
his declination 3° 41' south.

4. On the 31st of December, 1845, at 28 m. 55 sec.
past five o'clock in the evening, at Greenwich, there will
be an emersion of the first satellite of Jupiter ; where will
it be visible ? Jupiter's right ascension at that time will
be 1 h. 57 m., and longitude 0 sign 29° 8', and his declina-
tion 10° 40' south.

PROBLEM LVIII.

To place the terrestrial globe in the SUNSHINE, so that it
may represent the NATURAL POSITION of the earth.

RULE. If you have a meridian linef drawn upon a
horizontal plane, set the north and south points of the

* This is on supposition that Jupiter moves in the ecliptic, and
as he deviates but little therefrom, the solution by this method will be
sufficiently accurate. To know if an eclipse of any one of the satel-
lites of Jupiter will be visible at any place, we are directed by the
Nautical Almanac to " find whether Jupiter be 8° above the horizon
of the place, and the sun as much below it."

f As a meridian line is useful for fixing a horizontal dial, and for
placing a globe directly north and south, &c., the different methods of
drawing a line of this kind will precede the problems on dialling.

Chap. I. THE TERRESTRIAL GLOBE. 27?

wooden horizon of the globe directly over this line ; or,
place the globe directly north and south by the mariner's
compass, taking care to allow for the variation ; bring the
place in which you are situated to the brass meridian,
and elevate the pole to its latitude ; then the globe will
correspond in every respect with the situation of the earth
itself. The poles, meridians, parallel circles, tropics, and
all the circles on the globe, will correspond with the same
imaginary circles in the heavens ; and each point, king-
dom, and state, will be turned towards the real one, which ,
it represents.

While the sun shines on the globe, one hemisphere will
be enlightened, and the other will be in the shade : thus,
at one view, may be seen all places on the earth which
have day, and those which have night.*

If a needle be placed perpendicularly in the middle of
the enlightened hemisphere, (which must of course be
upon the parallel of the sun's declination for the given
day,) it will cast no shadow, which shews that the sun is
vertical at that point ; and if a line be drawn through this
point from pole to pole, it will be the meridian of the
place where the sun is vertical, and every place upon this
line will have noon at that time ; all places to the west of
this line will have morning, and all places to the east of
it afternoon. Those inhabitants who are situated on the
circle which is the boundary between light and shade, to
the westward of the meridian where the sun is vertical,
will see the sun rising; those in the same circle to the
eastward of this meridian will see the sun setting. Those
inhabitants towards the north of the circle, which is the
boundary between light and shade, will perceive the sun
to the southward of them, in the horizon ; and those who
are in the same circle towards the south, will see the sun
in a similar manner to the north of them.

If the sun shine beyond the north pole at the given
time, his declination is as many degrees north as he shines

* For this part of the problem it would be more convenient if the
globe could be properly supported without the frame of it, because the
shadow of its stand, and that of its horizon, will darken several parts
of the surface of the globe, which would otherwise be enlightened.

278 PROBLEMS PERFORMED BY Part III.

over the pole ; and all' places at that distance from the
pole will have constant day, till the sun's declination de-
creases, and those at the same distance from the south
pole will have constant night.

,If the sun do not shine so far as the north pole at the
given time, his declination is as many degrees south as
the enlightened part is distant from the pole ; and all
places within the shade, near the pole, will have constant
night, till the sun's declination increases northward.
While the globe remains steady in the position it was first
placed when the sun is westward of the meridian, you
may perceive on the east side of it, in what manner the
sun gradually departs from place to place as the night
approaches ; and when the sun is eastward of the meri-
dian, you may perceive on the western side of it, in what
manner the sun advances from place to place as the day
approaches.

PROBLEM LIX.

The latitude of a place being griven, to find the hour of the
day at any time when the SUN SHINES.

RULE 1. Place the north and south points of the
horizon of the globe directly north and south upon a
horizontal plane, by a meridian line, or by a mariner's
compass, allowing for the variation, and elevate the pole
to the latitude of the place ; then, if the place be in north
latitude, and the sun's declination be north, the sun will
shine over the north pole ; and if a long pin be fixed per-
pendicularly in the direction of the axis of the earth, and
in the centre of the hour circle, its shadow will fall upon
the hour of the day, the figure XII of the hour circle
being first set to the brass meridian. If the place be in
north latitude, and the sun's declination be above ten
degrees south, the sun will not shine upon the hour circle
at the north pole.

RULE 2. Place the globe due north and south upon a
horizontal plane, as before, and elevate the pole to the

Chap. I. THE TERRESTRIAL GLOBE. 279

latitude of the place ; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour circle to XII ; stick a needle perpendicularly in the
sun's place in the ecliptic, and turn the globe on its axis
till the needle casts no shadow ; fix the globe in this po-
sition, and the index will shew the hour before 12 in the
morning, or after 12 in the afternoon.

RULE 3. Divide the equator into 24 equal parts from
the point Aries, on which place the number VI ; and pro-
ceed westward VII, VIII, IX, X, XI, XII, I, II, III, IV,
V, VI, which will fall upon the point Libra, VII, VIII,
IX, X, XI, XII, I, II, III, IV, V * ; elevate the pole to
the latitude, place the globe due north and south upon a
horizontal plane, by a meridian line, or a good mariner's
compass, allowing for the variation, and bring the point
Aries to the brass meridian ; then observe the circle
which is the boundary between light and darkness west-
ward of the brass meridian ; and it will intersect the
equator in the given hour in the morning ; but, if the same
circle be eastward of the brass meridian, it will intersect
the equator in the given hour in the afternoon.

OR, Having placed the globe upon a true horizontal
plane, set it due north and south by a meridian line;
elevate the pole to the latitude, and bring the point Aries
to the brass meridian, as before ; then tie a small string,
with a noose, round the elevated pole, stretch its other
end beyond the globe, and move it so that the shadow of
the string may fall upon the depressed axis ; at that in-
stant its shadow upon the equator will give the hour, f

* On Adams* globes the antarctic circle is thus divided, by which
the problem may be solved.

f The learner must remember that the time shewn in this problem
is solar time, as shewn by a sun-dial ; and, therefore, to agree with a
good clock or watch, it must be corrected by a table of equation of
time. See a table of this kind among the succeeding problems.

280 PROBLEMS PERFORMED BY Part ill.

PROBLEM LX.

To find the suns altitude, by placing the globe in the SUN-
SHINE.

RULE. Place the globe upon a truly horizontal plane,
stick a needle perpendicularly over the north pole *, in
the direction of the axis of the globe, and turn the pole
towards the sun, so that the shadow of the needle may
fall upon the middle of the brass meridian ; then elevate
or depress the pole till the needle casts no shadow ; for
then it will point directly to the sun ; the elevation of the
pole above the horizon will be the sun's altitude.

PROBLEM LXI.

To find the sun's declination, his place in the ecliptic, and
his azimuth, by placing the globe in the SUN-SHINE.

RULE. Place the globe upon a truly horizontal plane,
in a north and south direction by a meridian line, and
elevate the pole to the latitude of the place ; then, if the
sun shine beyond the north pole, his declination is as
many degrees north as he shines over the pole ; if the sun
do not shine so far as the north pole, his declination is as
many degrees south as the enlightened part is distant
from the pole. The sun's decimation being found, his
place may be determined by Prob. XX.

Stick a needle in -the parallel of the sun's declination
for the given day f , and turn the globe on its axis till the
needle casts no shadow: fix the globe in this position,

* It would be an improvement on the globes were our instrument-
makers to drill a very small hole in the brass meridian over the north
pole.

•f On Adams' globes the torrid zone is divided into degrees by
dotted lines, so that the parallel of the sun's declination is instantly
found : in using other globes, observe the declination on the brass
meridian, and stick a needle perpendicularly in the globe under that
degree.

Chap. I. THE TERRESTRIAL GLOBE. 281

and screw the quadrant of altitude over the latitude ;
bring the graduated edge of the quadrant to coincide
with the sun's place, or the point where the needle is
fixed, and the degree on the horizon will show the
azimuth.

PROBLEM LXII.

To draw a meridian line * upon a horizontal plane, and to
determine the four cardinal points of the horizon.

RULE. Describe several circles from the centre of
the horizontal plane, in which centre fix a straight wire
perpendicular to the plane ; mark in the morning where
the end of the shadow touches one of the circles ; in the
afternoon mark where the end of the shadow touches the
same circle ; divide the arc of the circle contained be-
tween these two points into two equal parts ; a line drawn
from the point of division to the centre of the plane will
be a true meridian, or north and south line ; and if this
line be bisected by a perpendicular, that perpendicular
will be an east and west line ; thus you will have the four
cardinal points : but to be very exact, the plane must be
truly horizontal, the wire must be exactly perpendicular
to the plane, and the extremity of its shadow must be
compared, not only upon one of the circles, as above de-
scribed, but upon several of them.

PROBLEM LXIII.
To make a horizontal dial for any latitude.

DEFINITIONS AND OBSERVATIONS. — Dialling, or the
art of constructing dials, is founded entirely on astro-

* The method here given of drawing a meridian line evidently
supposes that the sun's declination does not change, during the inter-
val, between the observations. As, however, the sun's declination
undergoes a perceptible change in the space of four or six hours at
certain times of the year, (about the equinoxes, for instance,) it will be
proper, in order to avoid, as much as possible, any inaccuracy from
this cause, to make the observations about the time of the summer sol-
stice, at which season of the year the sun changes his declination so
slowly as to create no error worth regarding. — ED.

282 PROBLEMS PERFORMED BY Part III

nomy; and, as the art of measuring time is of the greatest
importance, so the art of dialling was formerly held in
the highest esteem, and the study of it was cultivated by
all persons who had any pretensions to science. Since
the invention of clocks and watches, dialling has not been
so much attended to, though it will never be entirely
neglected ; for, as clocks and watches are liable to stop and
go wrong, that unerring instrument, a true sun-dial, is
used to correct and to regulate them.

Suppose the globe of the earth to be transparent (as
represented by Fig. 4. in Plate II.), with the hour circles,
or meridians, &c. drawn upon it, and that it revolves
round a real axis NS, which is opaque and casts a shadow ;
it is evident that, whenever the edge of the plane of any
hour circle or meridian points exactly to the sun, the
shadow of the axis will fall upon the opposite hour circle
or meridian. Now, if we imagine any opaque plane to
pass through the centre of this transparent globe, the
shadow of half the axis NE will always fall upon one side
or other of this intersecting plane.

Let ABCD represent the plane of the horizon of London,
BN the elevation of the pole or latitude of the place ; so
long as the sun is above the horizon, the shadow of the
upper half NE of the axis will fall somewhere upon the
upper side of the plane ABCD. When the edge of the
plane of any hour circle, as F, G, H, i, K, L, M, o, points
directly to the sun, the shadow of the axis, which axis is
coincident with this plane, marks the respective hour line
upon the plane of the horizon ABCD : the hour line upon
the horizontal plane is, therefore, a line drawn from the
centre of it, to that point where this plane intersects the
meridian opposite to that on which the sun shines. Thus,
when the sun is upon F, the meridian of London, the
shadow of NE the axis will fall upon E, xn. By the
same method, the rest of the hour lines are found, by
drawing, for every hour a line from the centre of the
horizontal plane to that meridian, which is diametrically
opposite to the meridian pointing exactly to the sun. Ifj
when the hour circles are thus found, all the lines be
taken away except the semi-axis NE, what remains will
be a horizontal dial for the given place. From what

Ckap.l. THE TERRESTRIAL GLOBE. 283

has been premised, the following observations naturally
arise : —

1. The gnomon of every sun-dial must always be parallel
to the axis of the earth, and must point directly to the
two poles of the world.

2. As the whole earth is but a point when compared
with the heavens, therefore, if a small sphere of glass be
placed on any part of the earth's surface, so that its axis
be parallel to the axis of the earth, and the sphere have
such lines upon it, and such a plane within it as above
described ; it will show the hour of the day as truly as if
it were placed at the centre of the earth, and the body of
the earth were as transparent as glass.

3. In every horizontal dial the angle which the style,
or gnomon, makes with the horizontal plane, must always
be equal to the latitude of the place for which the dial is
made.

RULE FOR PERFORMING THE PROBLEM. — Elevate the

pole so many degrees above the horizon as are equal to
the latitude of the place ; bring the point Aries to the
brass meridian ; then, as globes in general * have meri .
dians drawn through every 15 degrees of longitude, east-
ward and westward from the point Aries, observe where
these meridians intersect the horizon, and note the num-
ber of degrees between each of them ; the arcs between
Jthe respective hours will be equal to these degrees. The
dial must be numbered XII at the brass meridian, thence
XI, X, IX, VIII, VII, VI, V, IV, &c. towards the west,
for morning hours ; and, I, II, III, IV, V, VI, VII, VIII,
&c. for evening hours. No more hour lines need be
drawn than what will answer to the sun's continuance
above the horizon on the longest day at the given place.
The style .or gnomon of the dial must be fixed in the
centre of the dial-plate, and make an angle therewith
equal to the latitude of the place. The face of the dial

* On Gary's large globes the meridians are drawn through every
ten degrees, an alteration which answers no useful purpose whatever,
and is in many cases very inconvenient. To solve this problem, by
these globes, meridians must be drawn through every fifteen degrees
with a pencil.

284-

PROBLEMS PERFORMED BY

Par/ III.

may be of any shape, as round, elliptical, square, oblong,
&c. &c.

EXAMPLE. To make a horizontal dial for the latitude
of London.

Having elevated the pole 51 lz deg. above the horizon, and brought
the point Aries to the brass meridian, you will find the meridians on
the eastern part of the horizon, reckoning from 12, to be 11° 5O',
24° 2C/, 38° 3', 53° 35', 71° 6', and 90°, for the hours I, II, III,
IV, V, and VI ; or, if you count from the east towards the south,
they will be 0°, 18° 54', 36° 25', 51° 57', 65° 4O7, and 78° lO', for
the hours VI, V, IV, III, II, I, reckoning from VI o'clock back-
ward to XII. There is no occasion to give the distances farther than
VI, because the distances from XII to VI in the forenoon are exactly
the same as from XII to VI in the afternoon; and hour lines con-
tinued through the centre of the dial are the hours on the opposite
parts thereof.

The following table, calculated by spherical trigonometry, contains
not only the hour arcs, but the halves and quarters from XII to VI : —

Hours.

Hour

Angles.

Hour

Arcs.

Hours.

Hour

Angles.

Hour
Arcs.

XII
!8f

0° 0'
3 45

0° 0'
2 56

S£
3£

48° 45'
52 30

41° 45'
45 34

12§

7 30

5 52

56 15

49 30

12|

11 15

8 51

60 0

53 35

15 0

11 50

63 45

57 47

18 45

14 52

67 30

62 6

22 30

17 57

71 15

66 33

26 15

21 6

75 0

71 6

30 0

24 W

78 45

75 .45

33 45

27 36

82 30

80 25

37 30

31 0

86 15

85 13

41 1.5

34 28

90 0

III

45 0

38 3

The calculation of the hour arcs by spherical trigonometry is ex-
tremely easy; for while the globe remains in the position above
described, it will be seen that a right angled spherical triangle is form-
ed, the perpendicular of which is the latitude, its base the hour arc,
and its vertical angle the hour angle. Hence,

Radius, sine of 90°

Is to sine of the latitude ;

As tangent of the hour angle,

Is to the tangent of the hour arc on the horizon.
.It may be observed here, that if a horizontal dial, which shows the

Chap. I. THE TERRESTRIAL GLOBE. 285

hour by the top of the perpendicular gnomon, be made for a place in
the torrid zone, whenever the sun's declination exceeds the latitude of
the place, the shadow of the gnomon will go back twice in the day,
once in the forenoon and once in the afternoon ; and the greater the
difference between the latitude and the sun's declination is, the farther
the shadow will go back. In the 38th chapter of Isaiah, Hezekiah is
promised that his life shall be prolonged 15 years, and as a sign of
this, he is also promised that the shadow of the sun-dial of Ahaz shall
go back ten degrees. This was truly, as it was then considered, a
miracle ; for, as Jerusalem, the place where the dial of Ahaz was
erected, was out of the torrid zone, the shadow could not possibly go
back from any natural cause.

PROBLEM LXIV.
To make a vertical dial facing the south, in north latitude.

DEFINITIONS AND OBSERVATIONS. — The horizontal
dial, as described in the preceding problem, was supposed
to be placed upon a pedestal, and as the sun always shines
upon such a dial when he is above the horizon, provided
no objects intervene, it is the most complete of all kinds of
dials. The next in utility is the vertical dial facing the
south in north latitudes ; that is, a dial standing against
the wall of a building which exactly faces the south.

Supposing the globe to be transparent, as in the fore-
going problem (see Figure 5. Plate II.), with the hour
circles or meridians F, G, H, i, K, L, M, o, &c. drawn upon
it ; ADCB an opaque vertical plane perpendicular to the
horizon, and passing through the centre of the globe.
While the globe revolves round its axis NS, it is evident
that, if the semi-axis ES be opaque and cast a shadow,
this shadow will always fall upon the plane ABC, and mark
out the hours as in the preceding problem. By com-
paring Fig. 5. with Fig.b. in Plate II. it will appear that
the plane surface of every dial whatever is parallel to the
horizon of some place or other upon the earth, and that
the elevation of the style or gnomon above the dial's sur-
face, when it faces the south, is always equal to the latitude
of the place whose horizon is parallel to that surface.
Thus it appears that SP, which is the co-latitude of Lon-

286 PROBLEMS PERFORMED BY Part III.

don, is the latitude of the place whose horizon is represented
by the plane ADCB : for, let the south pole of the globe be
elevated 38£ degrees above the southern point of the hori-
zon, and the point Aries be brought to the brass meridian ;
then, if the globe be placed upon a table, so as to rest on
the south point of the wooden horizon, it will have exactly
the appearance of Fig. 5. Plate II. ; the wooden horizon
will represent the opaque plane ADCB, the south point will
be at B, and the north point at D under London, the east
point at c, and the west point at A. Hence we have the
following

RULE FOR PERFORMING THE PROBLEM. If the

place be in north latitude, elevate the south pole to the
complement of that latitude; bring the point Aries to
the brass meridian; then supposing meridians to be
drawn through every 15° of longitude, eastward and
westward from the point Aries (as is generally the case),
observe where these meridians intersect the horizon, and
note the number of degrees between each of them ; the
arcs between the respective hours will be equal to these
degrees. The dial must be numbered XII, at the brass
meridian, thence XI, X, IX, VIII, VII, VI, towards the
west, for morning hours ; and I, II, HI, IV, V, VI, to-
wards the east, for evening hours. As the sun cannot
shine longer upon such a dial as this than from VI in the
morning to VI in the evening, the hour lines need not be
extended any farther.

EXAMPLE. To make a vertical dial for the latitude of
London.

Elevate the' south pole 38£ degrees above the horizon, and bring
the point Aries to the brass meridian; then the meridians will inter-
sect the horizon, reckoning from the south towards the east, in the
following degrees; 9° 28', 19° 45', 31° 54', 47° 9', 66° 42', and 90°,
for the hours I, II, III, IV, V, VI : or, if you count from the east
towards the south, they will be 0°, 23° 18', 42° 51', 58° &, 70° 15',
80° 32', for the hours VI, V, IV, III, II, I. The distances from
XII to VI in the forenoon are exactly the same as the distances from
XII to VI in the afternoon.

The following table contains not only the hour arcs, but the halves
and quarters from XII to VI ; it is calculated exactly in the same
manner as the table in the piecedirtg problem, using the complement
of the latitude instead of the latitude : —

Chap. I.

THE TERRESTRIAL GLOBE.

287

Hours.

Hour
Angles.

Hour
Arcs.

Hours.

Hour
Angles.

Hour
Arcs.

XII

0° 0'

48° 45'

35° 22/

1*|

12i
12f

3 45
7 30
11 15

2 20
4 41
7 3

52 30
56 15
60 0

39 S
42 58
47 9

15 0

9 28

63 45

51 36

18 45

11 56

67 30

56 20

22 30

14 27

71 15

61 23

26 15

17 4

75 0

66 43

30 0

19 45

5| ' 78 45

72 17

33 45

22 35

R2 30

78 3

37 30

25 32

86 15

84 0

41 15

28 38

90 0

III

45 0

31 54

The student will recollect that the time shown by a sun-dial is not
the exact time of the day, as shown by a watch or clock (see Defini-
tions 55, 56, and 57. , page 13.). A good clock measures time equally,
but a sun-dial (though used for regulating clocks and watches) mea-
sures time unequally. The following table will show to the nearest

288 PROBLEMS PERFORMED BY Part IIL

minute how much a clock should be faster or slower than a sun-dial ;
such a table should be put upon every horizontal sun-dial : —

Dials may be constructed on all kinds of planes, whether horizontal
or inclined ; a vertical dial may be made to face the south, or any
point of the compass ; but the two dials already described are the
most useful. To acquire a complete knowledge of dialling, the gno-
monical projection of the sphere, and the principles of spherical
trigonometry, must be thoroughly understood ; these preliminary
branches may be learned from Emerson's Gnomonical Projection, and
KeitKs Trigonometry. The writers on dialling are very numerous :
the last and best treatise on the subject is Emerson's.

CHAPTER II.
Problems performed by the Celestial Globe. *

PROBLEM LXV.

To find the right ascension and declination of the sun f , or
a star.

RULE. Bring the sun's place or the given star to that
part of the brass meridian which is numbered from the

* It would be well if all teachers of the use of the globes insisted
on their pupils making themselves thoroughly acquainted with the
letters of the Greek alphabet before they allowed them to commence
the problems on the celestial globe. And also if such teachers made
a practice of frequently directing the attention of their pupils to small
stars (say of the third, fourth, and fifth magnitudes). For want of
adopting this judicious practice, the editor has known many persons
to become tolerably well acquainted with stars of the first and second
magnitudes without knowing in what part of any constellation a star
of any of the inferior magnitudes was situated. Another error which
has tended, in no small degree, to confine the knowledge of the pupil
to a few of the principal stars only, and even of those merely by name,
is the very injudicious practice of writers on the use of the globes
always referring to stars which have proper names, and referring to
them by name ONLY, instead of by their Greek characters. The pre-
sent volume is not wholly exempt from these faults. The editor, how-
ever, has not thought it necessary to alter Mr. Keith's plan in this
respect, not doubting that the hint here given will be duly appreciated,
and render any such alteration unnecessary. — ED.

f The right ascensions and declinations of the moon and the planets
must be found from an ephemeris ; because, by their continual change
of situation, they cannot be placed on the celestial globe, as the stars
are placed.

Chap. II. THE CELESTIAL GLOBE. 289

equinoctial towards the poles; the degree on the brass
meridian is the declination, and the number of degrees on
the equinoctial, between the brass meridian and the point
Aries, is the right ascension. *

OR, Place both the poles of the globe in the horizon,
bring the sun's place or star to the eastern part of the
horizon ; then the number of degrees which the sun's place
or star is northward or southward of the east, will be the
declination north or south ; and the degrees on the equi-
noctial, from Aries to the horizon, will be the right as-
cension.

EXAMPLES. 1. Required the right ascension and de-
clination of a Dubke, in the back of the Great Bear

Answer. Right ascension lOh. 54m. or 163° 15', declination
62° 36' N.

2. Required the right ascensions and declinations of the
following stars ?

y, Algenib, in Pegasus. /3, Rigel, in Orion,

a, Scheder, in Cassiopeia. y, Bellatrix, in Orion.
/3, Mirach, in Andromeda.
a, Acherner, in Eridanus.
a, Menkar, in Cetus.
/5, Algol, in Perseus,
a, Aldebaran, in Taurus,
a, Capella, in Auriga.

f) JL-*l^l/l/W/l>» C*1*/J ill V/A, J.VA.J*

a, Betelgeux, in Orion,
a, Canopus, in Argo Navis.
a, Procyon, in theLittleDog.
a, Spica, in Virgo,
a, Arcturus, in Bootes,
a, Vega, in Lyra.

* Right ascension is reckoned from the first point of Aries eastward
quite round the globe. The right ascension of 100 principal fixed
stars will be found in the Nautical Almanac, the ascensions being ex-
pressed ill hours, minutes, and seconds of time ; which may, however,
be easily » educed to degrees, &c., allowing one hour of time to every
15°, four minutes of time to 1°, and four seconds of time to 1' of mo-
tion. Or right ascension in time may be reduced to degrees, minutes,
&c., by multiplying by 15 or its equal 5x3. Degrees, minutes, &c.
may be brought into time by dividing by 15. Examples : —

10h 53m 15)163° 15'

5x3^15

10h 13° 15'
60

15)795

163° 15'

O 53™

290 PROBLEMS PERFORMED BY Part III.

PROBLEM LXVI.
To find the latitude and longitude of a star.*

RULE. Place the upper end of the quadrant of alti-
tude on the north or south pole of the ecliptic, according
as the star is on the north or south side of the ecliptic, and
move the other end till the star comes to the graduated
edge of the quadrant : the number of degrees between the
ecliptic and the star is the latitude ; and the number of
degrees on the ecliptic, reckoned eastward from the point
Aries to the quadrant, is the longitude.

OR, Elevate the north or south pole 66£° above the
horizon, according as the given star is on the north or
south side of the ecliptic ; bring the pole of the ecliptic
to that part of the brass meridian which is numbered
from the equinoctial towards the pole ; then the ecliptic
will coincide with the horizon; screw the quadrant of
altitude upon the brass meridian over the pole of the
ecliptic ; keep the globe from revolving on its axis, and
move the quadrant till its graduated edge comes over the
given star : the degree on the quadrant cut by the star is
its latitude ; and the sign and degree on the ecliptic cut
by the quadrant shew its longitude.

EXAMPLES. 1. Required the latitude and longitude of
a, Aldebaran in Taurus ?

Answer. Latitude 5° 28' S. longitude 2 signs 6° 53' ; or 6° 53*
in Gemini.

2. Required the latitudes and longitudes of the follow-

ing stars ?

«, Markab, in Pegasus.

0, Scheat, in Pegasus.

a, Fomalhautjn the S.Fish.

a, Deneb, in Cygnus.

a, Altair, in the Eagle.

8, Albireo, in Cygnus.

a, Vega, in Lyra.

y, Rastaben, in Draco.

a, Antares, in the Scorpion,

a, Arcturus, in Bootes.

]3, Pollux, in Gemini.

jS, Rigel, in Orion.

* The latitudes and longitudes of the planets must be found from
an ephemeris.

Chap. II.

THE CELESTIAL GLOBE.

291

PROBLEM LXVIL

The right ascemion and declination of a star, the moon, a
planet, or of a comet, being given, to find its place on the
globe.

RULE. Bring the given time or degree of right ascen-
sion to that part of the brass meridian which is numbered
from the equinoctial towards the poles ; then under the
given declination on the brass meridian you will find the
star, or place of the planet.

EXAMPLES. 1. What star has 17 h. 26 m. or 261° 30'
of right ascension, and 52° 25' north declinatibn ?

Answer, ft in Draco.

2. On the 15th of June, 1845, the moon's right ascen-
sion at 6 o'clock in the morning will be 13 h. 12 m., and
her declination 10° 51' S. ; find her place on the globe at
that time.

Answer. She will be near to the star a Spica in Virgo.

3. What stars have the following right ascensions and
declinations ? The right ascension is given both in time
and measure.

Right Ascensions.

h. in.

0 31. or 7° 45'
11 11
25 54
46 32

046
1 45
3 8
335
5 6

53 54
76 34

Declinations.

55° 36' N.
59 48 N.
19 58 N.
9 27 S.
23 29 N.
8 24 S.

Right Ascensions,
h. m.
5 38 or 83° SO7
547 86 13
6 37 99 33
724 111 7
735 113 54
8 38 129 32

Declinations.

34° 10/ S.

44 55 N.

16 29 .S.

32 15 N.
28 25 N.

7 2 N.

4. On the 3d of December, 1843, the moon's right
ascension at midnight will be 2hrs. 18 roin., and her de-
clination 17°'47 N. ; find her place on the globe.

5. On the 1st of May, 1844, the declination of Venus
will be 26° 22' N., and her right ascension 5 hrs. 42 min. ;
find her place on the globe at that time.

6. On the 19th of July, 1845, the declination of Jupiter
will be 13° N., and his right ascension 2 hrs. 24 min. ;
find his place on the globe at that time.

o 2

PROBLEMS PERFORMED BY

Part III,

PROBLEM LXVIII.

The latitude and longitude of the moon, a star, or a planet,
given, to find its place on the globe.

RULE. Place the division of the quadrant of altitude
marked o, on the given longitude in the ecliptic, and the
upper end on the pole of the ecliptic ; then, under the
given latitude, on the graduated edge of the quadrant,
you will find the star, or place of the moon or planet

EXAMPLES. 1. What star has 0 sign 6° 16' of longi-
tude, and 12° 36' N. latitude ?

Answer, y in Pegasus.

2. On the 5th of June, 1845, at midnight, the moon's
longitude will be about 85° 23' or 25° 23' in n, and
her latitude 2° 37' S. ; find her place on the globe.

3. What stars have the following latitudes and longi-
tudes ?

Latitudes.
12° 35' S.
29 S,
8 S.
52 N.
3 S.

31
22
16

Longitudes.
Is 11° 25'
2 6 53
2 13 56
2 18 57
2 25 51

Latitudes.
39° 33' S.

10 4 N.

0 27 N.

44 20 N.

21 6 S.

Longitudes.
3« 11° 13'

3 17 21

4 26 57
7 9 22

11 0 56

4. On the 1st of June, 1845, the longitudes and lati-
tudes of the planets will be nearly as follow : required
their places on the globe ?

Longitudes.
$ 1s 18°
9 V* 15
$ 10^ 19J

; Longitudes.
II Is 0°

Latitudes.

iy s.
i s.

PROBLEM LXIX.

The day and hour, and the latitude of a place being given,
to find what stars are rising, setting, culminating, fyc.

RULE. Elevate the pole to the latitude of the place,
find the sun's place in the ecliptic, bring it to the brass
meridian, and set the index of the hour-circle to 12;
then, if the time be before noon, turn the globe eastward

Chap. II. THE CELESTIAL GLOBE* 293

on its axis till the index has passed over as many hours
as the time wants of noon ; but, if the time be past noon,
turn the globe westward till the index has passed over as
many hours as the time is past noon : then all the stars
on the eastern semi-circle of the horizon will be rising,
those on the western semi-circle will be setting, those
under the brass meridian above the horizon will be culmin-
ating, those above the horizon will be visible at the given
time and place, those below will be invisible.

If the globe be turned on its axis from east to west,
those stars which do not go below the horizon never set
at the given place ; and those which do not come above
the horizon never rise ; or, if the given latitude be sub-
tracted from 90 degrees, and circles be described on the
globe, parallel to the equinoctial, at a distance from it
equal to the degrees in the remainder, they will be the
circles of perpetual apparition and occultation.

EXAMPLES. 1. On the 9th of February, when it is
nine o'clock in the evening at London, what stars are
rising, what stars are setting, and what stars are on the
meridian ?

Answer. Alphacca, in the northern Crown is rising ; Arcturus and
Mirach, in Bootes, just above the horizon ; Sinus on the meridian ;
Procyon and Castor and Pollux a little east of the meridian. The
constellations Orion, Taurus, and Auriga, a little west of the meridian :
Markab, in Pegasus, just below the western edge of the horizon, &c.

2. On the 20th of January, at two o'clock in the morn-
ing at London, what stars are rising, what stars are set-
ting, and what stars are on the meridian ?

Answer. Vega in Lyra, the head of the Serpent, Spica Virginis,
£c. are rising ; the head of the Great Bear, the claws of Cancer, &c.
on the meridian ; the head of Andromeda, the neck of Cetus, and the
body of Columba Noachi, &c. are setting.

3. At fen o'clock in the evening at Edinburgh, on the
15th of November, what stars are rising, what stars are
setting, and what stars are on the meridian ?

4. What stars do not set in the latitude of London,
and at what distance from the equinoctial is the circle of
perpetual apparition ?

5. What stars do not rise to the inhabitants of Edin-
burgh, and at what distance from the equinoctial is (he
circle of perpetual occultation?

o 3

294 PROBLEMS PERFORMED BY Part IIL

6. What stars never rise at Otaheite, and what stars
never set at Jamaica ?

7. How far must a person travel southward from Lon-
don to lose sight of the Great Bear ?

8. What stars are continually above the horizon at the
north pole, and what stars are constantly below the hori-
zon thereof?

PROBLEM LXX.

The latitude of a place, day of the month, and hour being
given, to place the globe in such a manner as to represent
the heavens at that time ; in order to find out the relative
situations and names of the constellations and remarkable
stars.

RULE. Take the globe out into the open air, on a
clear starlight night, where the surrounding horizon is
uninterrupted by different objects ; elevate the pole to
the latitude of the place, and set the globe due. north and
south by a meridian line, or by a mariner's compass, taking
care to make a proper allowance for the variation ; find
the sun's place in the ecliptic, bring it to the brass meri-
dian and set the index of the hour-circle to 12; then,
if the time be after noon, turn the globe westward on its
axis, till the index has passed over as many hours as the
time is. past noon ; but, if the time be before noon, turn
the globe eastward till the index has passed over as many
hours as the time wants of noon ; fix the globe in this
position, then the flat end of a pencil being placed on any
star on the globe so as to point towards the centre, the
other end will point to that particular star in the heavens.

PROBLEM LXXI.

To find when any star, or planet, will rise, come to the
meridian, and set at any given place.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place ; find the

II. THE CELESTIAL GLOBE. 295

sun's place in the ecliptic, bring it to the brass meridian,
and set the index of the hour-circle to 12. Then if the
star * or planet be below the horizon, turn the globe west-
ward till the star or planet comes to the eastern part of
the horizon, the hours passed over by the index will show
the time from noon when it rises ; and, by continuing the
motion of the globe westward till the star, &c. comes to
the meridian, and to the western part of the horizon suc-
cessively, the hours passed over by the index will show
the time of culminating and setting.

If the star, &c. be above the horizon and east of the
meridian, find the time of culminating, setting, and rising
in a similar manner. If the star, &c. be above the hori-
zon west of the meridian, find the time of setting, rising,
and culminating, by turning the globe westward on its axis.

EXAMPLES. 1. At what time will Arcturus rise, come
to the meridian, and set, at London, on the 7th of Sep-
tember ?

Answer. It will rise at a quarter past seven o'clock in the morning,
come to the meridian at a quarter past three in the afternoon, and set
at a quarter before eleven o'clock at night

2. On the 16th of September, 1843, the right ascension
of Jupiter will be 21 hours 27 min., and his declination
16° 15' S.; at what time will he rise, culminate, and set,
at Greenwich, and whether will he be a morning or an
evening star ?

Answer. Jupiter will rise at five o'clock in the afternoon, come to
the meridian at about a quarter before ten in the evening, and set at
half past two in the morning. Here Jupiter will be an evening star,
because he will both rise and set after the sun.

3. At what time does Sirius rise, set, and come to the
meridian of London, on the 31st of January?

4. On the 22d of November, 1845, the right ascension
of Venus will be 19 hrs. 7 min., and her decimation 25° 15'
S. ; at what time will she rise, culminate, and set at
London, and whether will she be a morning or an evening
star?

* The latitude and longitude (or the right ascension and declin-
ation of the planet) must be taken from anephemeris, and its place on
the globe must be determined by Prob. LXVIII. (or LXVII.)
O 4

296 PROBLEMS PERFORMED BY Part III.

5. At what time does Aldebaran rise, come to the me-
ridian, and set at Dublin, on the 25th of November?

6. On the 10th of November, 1845, the right ascension
of Mars will be 22 hrs. 35 min., and his declination 10° 49'
S. ; at what time will he rise, set, and come to the

dian of Greenwich ?

PROBLEM LXXII.

To find t/ie amplitude of any star, its oblique ascension and
descension, and its diurnal arc for any given day.

RULE. Elevate the pole to the latitude of the place,
and bring the given star to the eastern part of the hori-
zon ; then the number of degrees between the star and
the eastern point of the horizon will be its rising am-
plitude ; and the degree of the equinoctial cut by the
horizon will be the oblique ascension : set the index of
the hour-circle to 12, and turn the globe westward till the
given star comes to the western edge of the horizon ; the
hours passed over by the index will be the star's diurnal
arc, or continuance above the horizon. The setting am-
plitude will be the number of degrees between the star
and the western point of the horizon, and the oblique de-
scension will be represented by that degree of the equi-
noctial which is intersected by the horizon, reckoning
from the point Aries.

EXAMPLES. 1. Required the rising and setting am-
plitude of Sirius, its oblique ascension, oblique descension,
and diurnal arc, at London ?

Answer. The rising amplitude is 27 deg. to the south of the east ;
setting amplitude 27 deg. south of the west; oblique ascension 120
deg. ; oblique descension 77 deg. ; and diurnal arc 9 hours 6 minutes,

2. Required the rising and setting amplitude of Alde-
baran, its oblique ascension, oblique descension, and diurnal
arc, at London ?

3. Required the rising and setting amplitude of Arctu-
rus, its oblique ascension, oblique descension, and diurnal
arc at London ?

4 Required the rising and setting amplitude of 7

II. THE CELESTIAL GLOBE. 29?

Bellatrix, its oblique ascension, oblique descension, and
diurnal arc, at London ?

PROBLEM LXXIIL

The latitude of a place given, to find the time of the year
at which any hnown star rises or sets ACRONICALLY, that
is, when it rises or sets at sun-setting.

RULE. Elevate the pole to the latitude of the place,
bring the given star to the eastern edge of the horizon,
and observe what degree of the ecliptic is intersected by
the western edge of the horizon, the day of the month
answering to that degree will shew the time when the
star rises at sun-set, and consequently when it begins to
be visible in the evening. Turn the globe westward on its
axis till the star comes to the western edge of the hori-
zon, and observe what degree of the ecliptic is inter-
sected by the horizon as before ; the day of the month
answering to that degree will shew the time when the
star sets with the sun, or when it ceases to appear in the
evening.

EXAMPLES. 1. At what time does Arcturus rise
acronically at Ascra* in Boeotia, the birth-place of
Hesiod; the latitude of Ascra, according to Ptolemy,
being 37 deg. 45 min. N. ?

Answer. When Arcturus is at the eastern part of the horizon, the
eleventh degree of Aries will be at the western part answering to the
first of April f, the time when Arcturus rises acronically ; and it will
set acronically on the 30th of November.

* See page 16.

f Hence Arcturus now rises acronically in latitude 37° 45' N.
about 100 days after the winter solstice. Hesiod, in his Opera $ Dies,
lib. ii. verse 185. says:

When from the solstice sixty wintry days
Their turns have finished, mark, with glittering rays,
From Ocean's sacred flood Arcturus rise,
Then first to gild the dusky evening skies.

Here is a difference of 40 days in the acronical rising of this star
(supposing Hesiod to be correct) between the time of Hesiod and
O 5

298 PROBLEMS PERFORMED BY Part III.

2. At what time of the year does Aldebaran rise
acronically at Athens, in 38 deg. N. latitude ; and at
what time of the year does it set acronically ?

3. On what day of the year does y in the extremity of
the wing of Pegasus rise acronically at London ; and on
what day of the year does it set acronically ?

4. On what day of the year does e in the right foot of
Lepus rise acronically at London ; and on what day of
the year does it set acronically ?

PROBLEM LXX1V.

The latitude of a place given, to find the time of the year at
which any known star rises or sets COSMICALLY, that w,
when it rises or sets at sun-rising.

RULE. Elevate the pole to the latitude of the place,
bring the given star to the eastern edge of the horizon,
and observe what sign and degree of the ecliptic are in-
tersected by the horizon; the month and day of the
month, answering to that sign and degree, will shew the
time when the star rises with the sun. Turn the globe
westward on its axis till the star comes to the western
edge of the horizon, and observe what sign and degree
of the ecliptic are intersected by the eastern edge, as be-
fore ; these will point out on the horizon the time when
the star sets at sun-rising.

EXAMPLES. 1. At what time of the year do the
Pleiades set cosmically at Miletus in Ionia, the birth-
place of Thales ; and at what time of the year do they rise
cosmically ; the latitude of Miletus, according- to Ptolemy,
being 37 deg. N.?

the present time ; and as a day answers to about 59' of the ecliptic
(see the note page 15.) 40 days will answer to 39 deg. ; consequently,
the winter solstice in the time of Hesiod was in the 9th deg. of Aqua-
rius. Now, the recession of the equinoxes is about 50{" in a year ;
hence 50^": 1 year : : 39° : 2794 years since the time of Hesiod ,
so that he lived 952 years before Christ, by this mode of reckoning.
Lempriere in his Classical Dictionary says Hesiod lived 907 years
before Christ.

Chap. II. THE CELESTIAL GLOBE. ^99

Answer. The Pleiades rise with the sun on the llth of May, and
they set at the time of sun-rising on the 23d of November. *

2. At what time of the year does Sirius rise with the
sun at London ; and at what time of the year will Sirius
set when the sun rises ?

3. At what time of the year does Menkar, in the jaw
of Cetus, rise with the sun, and at what time does it set
at sun-rising at London ?

4. At what time of the year does Procyon, in the
Little Dog, set when the sun rises at London, and at
what time of the year does it rise with the sun ?

PROBLEM LXXV.
To find the time of tfte year when any given star rises or

SetS HELIACALLY. f

RULE. The heliacal rising and setting of the stars will
vary according to their different degrees of magnitude
and brilliancy ; for it is evident that the brighter a star
is when above the horizon the less the sun will be
depressed below the horizon when that star first be-
comes visible. According to Ptolemy, stars of the first
magnitude are seen rising and setting when the sun is
twelve degrees below the horizon; stars of the second

* Pliny says (Nat. Hist. lib. xvjii. cap. 25.) that Thales determined
the cosmical setting of the Pleiades to be twenty-five days after the
autumnal equinox. Supposing this observation to be made at Miletus,
there will be a difference of thirty-five days in the cosmical setting of
this star since the time of Thales ; and, as a day answers to about 59'
of the ecliptic, these days will make about 34° 25' ; consequently, in
the time of Thales, the autumnal equinoctial colure passed through
4° 25" of Scorpio ; and, as before, 50f : 1 year : : 34° 25' : 2465 years
since the time of Thales, so that Thales lived (2465 — 1844) 621
years before the birth of Christ. According to Sir I. Newton's
Chronology, Thales flourished 596 before Christ. Thales was well
skilled in geometry, astronomy, and philosophy ; he measured the
height and extent of the Pyramids of Egypt, was the first who calcu-
lated with accuracy a solar eclipse ; he discovered the solstices and
equinoxes, divided the heavens into five zones, and recommended the
division of the year into 365 days. Miletus was situated in Asia Minor,
south of Ephesus, and south-east of the island of Samos.

t See Definition 90. page 26.

o 6

300 PROBLEMS PERFORMED BY Part III.

magnitude require the sun's depression to be thirteen
degrees ; stars of the third magnitude fourteen degrees,
and so on, reckoning one degree for each magnitude.
This being premised :

To SOLVE THE PROBLEM. Elevate the pole so many
degrees above the horizon as are equal to the latitude of
the place, and screw the quadrant of altitude on the
brass meridian over that latitude; bring the given star
to the eastern edge of the horizon, and move the quadrant
of altitude till it intersects the ecliptic twelve degrees
below the horizon, if the star be of the first magni-
tude ; thirteen degrees, if the star be of the second
magnitude ; fourteen degrees, if it be of the third mag-
nitude, &c. : the point of the ecliptic, cut by the quadrant,
will shew the day of the month, on the horizon, when the
star rises heliacally. Bring the given star to the western
edge of the horizon, and move the quadrant of altitude
till it intersects the ecliptic below the western edge of
the horizon, in a similar manner as before ; the point of
the ecliptic cut by the quadrant will shew the day of the
month, on the horizon, when the star sets heliacally.

EXAMPLES. 1. At what time does /2 Tauri, or the
bright star in the Bull's Horn, of the second magnitude,
rise and set heliacally at Rome ?

Answer. The quadrant will intersect the 3d of Cancer 13 degrees
below the eastern horizon, answering to the 24th of June ; and the 7th
of Gemini 1 3 deg. below the western horizon, answering to the 28th
of May.

2. At what time of the year does Sirius, or the Dog
Star, rise heliacally at Alexandria in Egypt ; and at what
time does it set heliacally at the same place ?

Answer. The latitude of Alexandria is 3 1 deg. 1 3 min. north ; the
quadrant will intersect the 12th of Leo, 12 deg. below the eastern
horizon, answering to the 4th of August* ; and the 2d of Gemini, 12
deg. below the western horizon, answering to the 23d of May.

* The ancients reckoned the beginning of the Dog Days from the
heliacal rising of Sirius, and their continuance to be about 40 days.
Hesiod informs us that the hottest season of the year (Dog Days)
ended about 50 days after the summer solstice. We have determined
in the note of Example 1. Prob. LXXIII. (though perhaps not very

Chap. II. THE CELESTIAL GLOBE. 301

3. At what time of the year does Arcturus rise helia-
cally at Jerusalem, and at what time does it set heliacally ?

4. At what time of the year does Cor Hydrae rise and
set heliacally at London ?

5. At what time of the year does Procyon rise and set
heliacally at London ?

6. If the precession of the equinoxes be 50£ seconds
in a year, how many years will elapse, from 1845 before
Sirius, the Dog Star, will rise heliacally at Christmas, at
Cairo in Egypt ? * When this period happens, Sirius will
perhaps no longer be accused of bringing sultry weather.

accurately) , that the winter solstice, in the time of Hesiod, was in the
9th degree of Aquarius ; consequently, the summer solstice was in the
9th degree of Leo : now, it appears from above, that Sirius rises
heliacally at Alexandria when the sun is in the 12th degree of Leo ;
and, as a degree nearly answers to a day, Sirius rose heliacally in the
time of Hesiod, about four days after the summer solstice ; and if the
Dog Days continued forty days, they ended about forty-four days
after the summer solstice. The Dog Days in our almanacs begin
on the third of July, which is twelve days after the summer solstice,
and end , on the llth of August, which is fifty-one days after the
summer solstice ; and their continuance is thirty-nine days. Hence
it is plain, that the Dog Days of the moderns have no reference
whatever to the rising of Sirius, for this star rises heliacally at London
on the twenty-fifth of August and, as well as the rest of the stars,
varies in its rising and setting according to the variation of the
latitudes of places, and therefore it could have no influence whatever
on the temperature of the atmosphere ; yet, as the Dog Star rose
heliacally at the commencement of the hottest season in Egypt, Greece,
&c. in the earlier ages of the world, it was very natural for the ancients
to imagine that the heat, &c. was the effect of this star. A few years
ago, the Dog Days in our almanacs began at the Cosmical rising of
Procyon, viz. on the 30th of July, and continued to the 7th of Sep-
tember ; but they are now, very properly, altered, and made not to
depend on the variable rising of any particular star, but on the summer
solstice.

* This question is of too delicate a nature to admit of a correct
solution by a globe : the answer given to it in the key is, therefore,
merely an approximation to the truth. — ED.

302 PROBLEMS PERFORMED BY Part

PROBLEM LXXVI.

The latitude of a place and day of the month being given, to
find all those stars that rise and set ACRONICALLY,

COSMICALLY, and HELIACALLY. *

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the given place.
Then,

1. For the acronical rising and setting, find the sun's
place in the ecliptic, and bring it to the western edge of
the horizon, and all the stars along the eastern edge of
the horizon will rise acronically, while those along the
western edge will set acronically.

2. For the cosmical rising and setting, bring the sun's
place to the eastern edge of the horizon, and all the stars
along that edge of the horizon will rise cosmically, while
those along the western edge will set cosmically.

3. For the heliacal rising and setting, screw the quadrant
of altitude over the latitude, turn the globe eastward on
its axis till the sun's place cuts the quadrant twelve de-
grees below the horizon ; then all stars of the first mag-
nitude, along the eastern edge of the horizon, will rise

* This problem is the reverse of the three preceding problems.
Their principal use is to illustrate several passages in the ancient
writers, such as Hesiod, Virgil, Columella, Ovid, Pliny, &c. See
Definition 64. page 15, The knowledge of these poetical risings and
settings of the stars was held in great esteem among the ancients, and
was very useful to them in adjusti-ng the times set apart for their re-
ligious and civil duties, and for marking the seasons proper for the
several parts of husbandry ; for the knowledge of which the ancients
had of the motions of the heavenly bodies was not sufficient to adjust
the true length of the year ; and, as the returns of the seasons depend
upon the approach of the sun to the tropical and equinoctial points, so
they made use of these risings and settings to determine the commence-
ment of the different seasons, the time of the overflowing of the Nile,
&c. The knowledge which the moderns have acquired of the motions
of the heavenly bodies renders such observations as the ancients at-
tended to in a great measure useless, and, instead of watching the
rising and setting of particular stars for any remarkable season, they
can sit by the fire-side and consult an almanac.

Chap. II. THE CELESTIAL GLOBE.

heliacally ; and, by continuing the motion of the globe
eastward till the sun's place intersects the quadrant in
13, 14, 15, &c. degrees below the horizon, you will find
all the stars of the second, third, fourth, &c. magnitudes,
which rise heliacally on that day. By turning the globe
westward on its axis, in a similar manner, and bringing the
quadrant to the western edge of the horizon, you will find
all the stars that set heliacally.

EXAMPLES. 1. What stars rise and set cosmically at
Edinburgh, on the llth of June?

Answer. The bright star in Castor, Aldebaran in Taurus, Fomal-
haut in the southern Fish, &c. rise cosmically ; those stars in the body
of Leo Minor, the arm of Virgo, the right foot of Bootes, part of the
Centaur, &c. set cosmically.

2. What stars rise and set acronically at Drontheim in
Norway, latitude 63° 26' N. on the 18th of May?

Answer. Altair in the Eagle, the head of the Dolphin, &c. rise
acronically ; and Aldebaran in Taurus, Betelgeux in Orion, &c. set
acronically.

3. What star of the first magnitude rises heliacally at
London, on the 7th of October ?

4. What star of the first magnitude sets heliacally at
London, on the 5th of May ?

5. What stars rise and set acronically at London, on
the 26th of September ?

6. What stars rise and set cosmically at London, on
the 23d of March?

PROBLEM LXXVII.
To illustrate the precession of the equinoxes.

OBSERVATIONS. All the stars in the different con-
stellations continually increase in longitude ; consequently
either the whole starry heavens have a slow motion
from west to east, or the equinoctial points have a slow
motion from east to west. In the time of Meton *, the

* Meton was a famous mathematician of Athens, who nourished
about 1430 years before Christ. In a book called Enneadec»terides or

304? PROBLEMS PERFORMED BY Part III.

first star in the constellation Aries, now marked j3, passed
through the vernal equinox, whereas it is now upwards of
30 * degrees to the eastward of it.

ILLUSTRATION. Elevate the north pole 90 degrees
above the horizon, then will the equinoctial coincide with
the horizon ; bring the pole f of the ecliptic to that part
of the brass meridian which is numbered from the north
pole towards the equinoctial, and make a mark upon the
brass meridian above it ; let this mark be considered as
the pole of the world, let the equinoctial represent the
ecliptic, and let the ecliptic be considered as the equi-
noctial; then c.ount 38£ degrees, the complement of
the latitude of London, from this pole upwards, and
mark where the reckoning ends, which will be at 75 de-
grees, on the brass meridian, from the southern point of
the horizon ; this mark will stand over the latitude of
London.

Now turn the globe gently on its axis from east to
west, and the equinoctial points will move the same way,
while, at the same time, the pole of the world J will de-
scribe a circle round the pole of the ecliptic || of 46° 56'
in diameter ; this circle will be completed in a § Platonic
year, consisting of 25, 868 years, at the rate of 50*1 seconds
in a year, and the pole of the heavens will vary its situ-

cycle of 1 9 years, he endeavoured to adjust the course of the sun and
of the moon ; and attempted to show that the solar and lunar years
would regularly begin from the same point in the heavens.

* If the precession of the equinoxes be 50" *1 in a year, and if the
equinoctial colure passed through # Arietis 430 years before Christ,
the longitude of this star ought in 1844 to be 31° 38' 47"; for 1
year : 50"-1 :: 2274 years (=430 + 1844) : 31° 38' 47", and this
longitude is not far from the truth.

f The pole of the ecliptic is that point on the globe, in the arctic
circle, where the circular lines meet.

| Let it be remembered that the pole of the ecliptic on the globe
here represents the pole of the world.

|| Take notice, that the extremity of the globe's axis here represents
the pole of the ecliptic.

§ A Platonic year is a period of time determined by the revolution
of the equinoxes ; this period being once completed, the ancients were
of opinion that the world was to begin anew, and the same series of
things to return over again. See the 64th Definition, page 15.

Chap. II. THE CELESTIAL GLOBE. 305

ation a small matter every year. When 12,934J years,
being half the Platonic year, are completed, (which may
be known by turning the globe half round, or till the point
Aries coincides with the eastern point of the horizon,)
that point of the heavens which is now 8£ degrees south
of the zenith of London will be the north pole *, as may
be seen by referring to the mark which was made over
75 degrees on the meridian.

PROBLEM LXXVIIL
To find tfie distances of the stars from each other in degrees.

RULE. Lay the quadrant of altitude over any two
stars, so that the division marked o may be on one of the
stars ; the degrees between them will shew their distance,
or the angle which these stars subtend, as seen by a spec*
tator on the earth.

EXAMPLES. 1. What is the distance between Vega in
Lyra, and Altair in the Eagle ?

Answer. 34 degrees.

2. Required the distance between /3 in the Bull's Horn,
and 7 Bellatrix in Orion's shoulder ?

3. What is the distance between j3 Pollux in Gemini
and a in Canis Minor?

4-. What is the distance between r/, the brightest of the
Pleiades, and /3 in Canis Major ?

5. What is the distance between e in Orion's girdle,
and £ in Cetus ?

6. What is the distance between Arcturus in Bootes,
and Regulus in Leo ?

PROBLEM LXXIX.

To find what stars lie in or near the moons path, or what
stars the moon can eclipse, or make a near approach to.

RULE. Find the moon's longitude and latitude, or her
right ascension and declination, in an ephemeris, for
several days, and mark the moon's places on the globe (as
directed in Problems LXVIII. or LXVII.) ; then by lay-
ing a thread, or the quadrant of altitude, over these

* See page 134,

306 PROBLEMS PERFORMED BY Part III.

places, you will see nearly the moon's path *, and, conse*
quently, what stars lie in her way.

EXAMPLES. 1. What stars will be in or near the moon's
path, on the 28th, 29th, 30th, and 31st of March, 1844 ?
}) 's Longitude at Midnight. Latitude.

28th, '112° 43' or 25 22° 43' - - 3° 10' S.

29th, 125 37 - SI 5 37 - - 3 50 S.

30th, 138 58 - a 18 58 - - 4 30 S.

31st, 152 49 - t# 2 49 - - 4 55 S.

Answer. The stars will be found to be e and 5 Geminorum, 6, and
5 Cancri, ir Leonis, &c.

2. On the 7th, 8th, 9th, 10th, and llth of December,
1845, what stars will lie near the moon's path, her right as-
cension f and declination at midnight of the days annexed
being as under ?

7th, D 's right ascension Oh 29m declination 6° 34' N.

8th, - - 1 19 - 10 40 N.

9th, 2 10 - 14 11 N.

10th, - - 31 - 16 59 N.

llth, i/: -. ; - 3 52 - - 18 58 N.

PROBLEM LXXX.

Given the latitude of the place and the day of the month, to
find what planets will be above the horizon after sunsetting.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place ; find the
sun's place in the ecliptic, and bring it to the western
part of the horizon, or to ten or twelve degrees below ;
then look in the Ephemeris for that day and month, and

* The situation of the moon's orbit for any particular day may be
found thus : find the place of the moon's ascending node in the Ephe-
meris, mark that place and its antipodes (being the descending node)
on the globe ; half the way between these points make marks 5° 2&
on the north and south side of the ecliptic, viz. let the northern mark
be between the ascending and descending node, and the southern be-
tween the descending and ascending node ; a thread tied round these
four points will show the position of the moon's orbit.

f In this example the right ascension is given (in time) to the
nearest minute, and the declination to the nearest minute of a degree.
This mode of expressing the right ascension, viz. in time, is agreeable
to the form of the Nautical Almanac

Chap. II. THE CELESTIAL GLOBE. 307

you will find what planets are above the horizon ; such
planets will be fit for observation on that night.

EXAMPLES. 1. What planets will be visible after the
sun has descended ten degrees* below the horizon of
London, on the 12th of November, 1844? Their right
ascensions and declinations being as follow : —

Right Ascension. Declination. j| Right Ascension. Declination.

$ 15h 3m 17° 11' S. "M- 23h 41m 3° 42'S.i f

$1232 1 34 S, T? 20 17 20 22 S. II

$ 13 0 5 18 S. I $ 0 11 0 24N.J^
Answer. Jupiter, Saturn, and Herschel.

2. What planets will be above the horizon of London
when the sun has descended ten degrees below, on the
25th of December, 1845 ? Their right ascensions and
declinations being as follow : —
Right Ascension. Declination. 1 1 Right Ascension. Declination.

$ 18h38x 21°20'S. H. Ih57' 10° 37' N.
2 21 35 15 56 S. T? 21 16 17 4 S.

$ 08 0 40 N. I $ 0 25 1 54 N.

PROBLEM LXXXI.

Given the latitude of the place, day of the month) and hour
of the night or morning, to find what planets will be
visible at that hour.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place : find the
sun's place in the ecliptic, bring it to the brass meridian,
and set the index of the hour-circle to 12 ; then, if the
given time be before noon, turn the globe eastward till
the index has passed over as many hours as the time
wants of noon : but if the given time be past noon, turn
the globe westward on its axis till the index has passed

* The planets are not visible till the sun is a certain number of de-
grees below the horizon, and these degrees are variable according to
the brightness of the planets. Mercury becomes visible when the sun
is about 10 deg. below the horizon ; Venus when the sun's depression
is 5 degrees; Mars 11° 30'; Jupiter 8°; Saturn 10°; and the
Georgian 17° 30'.

308 PROBLEMS PERFORMED BY Part III.

over as many hours as the time is past noon ; let the
globe rest in this position, and look in the Nautical
Almanac for the right ascension and declination of the
planets * ; then, if any of them be in the signs which are
above the horizon, such planets will be visible.

EXAMPLES. 1. On the 1st of September, 1844, the
right ascension and declination of the planets, by the
Nautical Almanac, will be as follows : will any of them
be visible at London at five o'clock in the morning ?
Right Ascension. Declination. I] Right Ascension. Declination.
$ 12h 19m 4°30'S. 1J. Oh 8«> 0°51'S.'

7 56 15 38 N.
10 10 12 34- N.

20 16 20
0 21

0051XS."1 a

0 25 S. \ I

1 24 N. J *

Answer. Jupiter, Venus, and Mars.

2. On the 1st of November, 1845, the right ascensions
and declinations of the planets, as given in the Nautical
Almanac, are as follow : will any of them be visible at
London at seven o'clock in the evening ?

Right Ascension. Declination.

5 14h 40m 150 43' s.

$ 17 20 25 24 S.

<? 22 20 12 49 S.

Right Ascension. Declination.
2h 14m 11°56'N.

21 1 18 7
0 27 29

N.I
S. I
N.J

PROBLEM LXXXII.

The latitude of the place and day of the month being given,
to find how long Venus rises before the sun when she is a
morning star, and how long she sets after the sun when
she is an evening star.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place ; find the
right ascension and declination of Venus in the Nautical
Almanac, and mark her place on the globe ; find the sun's
place in the ecliptic, and bring it to the brass meridian ;
then, if the place of Venus be to the right hand of the

* As the longitude and latitude are not given in the Nautical Al-
manac, the editor of the present edition has frequently introduced the
right ascension and declination, instead of, as formerly, the longitude
and latitude.

Chap. II. THE CELESTIAL GLOBE. 309

meridian, she is an evening star ; if to the left hand, she is
a morning star

When Venus is an evening star. Bring the sun's place
to the western edge of the horizon, and set the index of
the hour-circle to 12; turn the globe westward on its axis
till Venus coincides with the western edge of the horizon ;
and the hours passed over by the index will show how
long Venus sets after the sun.

When Venus is a morning star. Bring the sun's place
to the eastern edge of the horizon, and set the index of
the hour-circle to 12; turn the globe eastward on its axis
till Venus comes to the eastern edge of the horizon, and
the hours passed over by the index will show how long
Venus rises before the sun.

NOTE. The same rule will serve for Jupiter^ by marking
his place instead of that of Venus.

EXAMPLES. 1. On the 1st of May, 1844, the right
ascension of Venus will be 5 hours 42 min., or 2 signs 26°,
or 26° in Gemini, declination 26° 22' N. ; will she be a
morning or an evening star ? If a morning star, how long
will she rise before the sun at London? If an evening
star, how long will she be above the horizon after the sun
has set ?

Answer. Venus will be an evening star, and will set about four
hours after the sun.

2. On the 1st of December, 1845, the right ascension
of Venus will be 19 hours 51 min., and her declination
23° 38' S ; will she be a morning or an evening star?
If a morning star, how long will she rise before the sun
at London ? If an evening star, how long will she be
above the horizon after the sun is set ?

3. On the 1st of January, 1846, the right ascension of
Jupiter will be 1 hour 57 minutes, and his declination
10° 40' N. ; will he be a morning or an evening star? If
a morning star, how long will he rise before the sun at
London ? If an evening star, how long will he be above
the horizon after the sun has set ?

310 PROBLEMS PERFORMED BY Part III

PROBLEM LXXXIII.

The latitude of a place and day of the month* being given,
to find the meridian altitude of any star or planet.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the given place ;
then,

For a star. Bring the given star to that part of the
brass meridian which is numbered from the equinoctial
-towards the poles ; the degrees on the meridian contained
between the star and the horizon will be the altitude
required.

For the moon or a planet. Look in an ephemeris for
the planet's right ascension and declination for the given
month and day, and mark its place on the globe (as in
Prob. LXVIL); bring the planet's place to the brass
meridian ; and the number of degrees between that place
and the horizon will be the altitude.

EXAMPLES. 1. What is the meridian altitude of Alde-
baran in Taurus, at London ? Ans. 54^°.

2. What is the meridian altitude of Arcturus in Bootes
at London ?

3. On the 5th of March, 1845, the right ascension of
Jupiter •(• will be 22 h. 53 min., and declination 8 degrees
1 1 min. south ; what will his meridian altitude be at
London ?

4. On the 6th of November, 1845, the right ascension
of Saturn will be 21 deg. 2 min., and declination 18 deg.
5 min. south ; what will be his meridian altitude at
London ?

5. On the 18th of April, 1845, at the time of the moon's
passage over the meridian of Greenwich, her right ascension

* The meridian altitudes of the stars on the globe, in the same lati-
tude, are invariable ; therefore when the meridian altitude of a star is
sought, the day of the month need not be attended to.

•(• The places of the planets may be taken out of the ephemeris for
noon without sensible error, because their declinations vary less than
that of the moon.

Chap. II. THE CELESTIAL GLOBE. 311

will be 10 hours 56 min., and declination 1° 29' N. ; re-
quired her meridian altitude at Greenwich?*

6. Required the moon's meridian altitude on the 1st of
January, 1846 ; the right ascension being 22 hours
4 min., and declination 6° 38' south ?

Note. This problem may be performed without a globe
having the latitude of the place, and the star or planet's
declination, as Problem XLI. For by taking the de-
clination in the last example from the co-latitudef of
London, we have 38° 30' — 6° 38' = 31° 52'.

PROBLEM LXXXIV.

To find all those places on the earth to which the moon will
be nearly vertical on any given day.

RULE. Look in an ephemeris, or the Nautical Alma-
nac, for the moon's latitude and longitude for the given
day, and mark her place on the globe (as in Prob. LXVIII.) ;
bring this place to that part of the brass meridian which is
numbered from the equinoctial towards the poles, and
observe the degree above it ; for all places on the
earth having that latitude will have the moon vertical
(or nearly so) when she comes to their respective me-
ridians.

* By the Nautical Almanac, page IV. of the month, the moon will
transit the meridian at 9 hrs. 8 min., or, neglecting the minutes,
9 hrs. Then, turning to page IX. of the same month, we find her
right ascension at 'that time to be 10 hrs. 56 min., and her declination
1° 29' or 1£° nearly, from which the meridional altitude may be ob-
tained as near the truth as the operation by a globe will admit ; or,
without the globe, the declination 1£° + 38^° (the co-lat. of London)
= 40°, the }) 's meridian altitude.

The moon will have the greatest and least meridian altitude to all
the inhabitants north of the equator, when her ascending node is in
Aries ; for her orbit making an angle of 5£° with the ecliptic, her
greatest altitude will be 5£° more than the greatest meridional altitude
of the sun, and her least meridional altitude 5£° less than that of the
sun. The greatest altitude of the sun at London is 62°; the moon's
greatest altitude is therefore 67° 2O7. , The least meridional altitude
of the sun at London is 15° ; the least meridional altitude of the moon
is therefore 9° 407.

f The co-latitude (complement of latitude) of any place is what it
wants of being 90 degrees. For example, the lat. of London is 51°
SO' ; therefore the co-lat. = 90°— 51° 30'= 38° 30', or 38J°.

312 PROBLEMS PERFORMED BY Part III.

OR : Take the moon's declination from page V. *, &d.
of the Nautical Almanac, and mark whether it be north
or south ; then, by the terrestrial globe, or by a map,
find all places having the same number of degrees of lati-
tude as are maintained in the moon's declination, and those
will be the places to which the moon will be successively
vertical on the given day. If the moon's declination
be north, the places will be in north latitude, and vice
versa.

EXAMPLES. 1. On the 8th of October, 184-5, the
moon's longitude at midnight will be 9 signs 22 deg.
25 min., and her latitude 4 deg. 44 min. north ; over what
places will she pass nearly vertically ?

Answer. She will be nearly vertical to all places that have 16° 54'
south lat. Hence, she will be nearly vertical to the southern parts of
New Holland ; the south of Madagascar, Angora, and Cape Negro,
in Africa; and Porto Seguro, South America.

2. On the 9th of December, 184-5, the moon's declination
at midnight will be 14i° N. nearly ; over what places on
the earth will she pass nearly vertical ?

3. What is the greatest north declination which the
moon can possibly have, and to what places will she be
then vertical ?

PROBLEM LXXXV.

Given the latitude of a place, day of the month, and the
altitude of a star, to find the hour of the night, and the
stars azimuth.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude upon the brass meridian
over that latitude : find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to 12 ; bring the lower end of the quadrant
of altitude to that side of the meridian f on which the

* The right ascension and declination of the moon for every hour
commence with page V. and end at page XII. of each month in the
Nautical Almanac.

f It is necessary to know on which side of the meridian the star is
at the time of observation, because it will have the same altitude on

Chap, II. THE CELESTIAL GLOBE. 313

star was situated when observed ; turn the globe westward
till the centre of the star cuts the given altitude on the
quadrant; count the hours which the index has passed
over, and they will show the time from noon when the
star has the given altitude : the quadrant will intersect
the horizon in the required azimuth.

EXAMPLES. 1. At London, on the 28th of December,
the star Deneb in the Lion's tail, marked /3, was observed
to be 40 deg. above the horizon, and east of the meridian ;
what hour was it, and what was the star's azimuth?

Answer. By bringing the sun's place to the meridian, and turning
the globe westward on its axis till the star cuts 40 deg. of the qua-
drant east of the meridian, the index will have passed over 14^ hours;
consequently, the star has 40 deg. of altitude east of the meridian, 1 4
hours from noon, or at a quarter past two o'clock in the morning. Its
azimuth will be 601 deg. from the south towards the east.

2. At London, on the 28th of December, the star jB, in
the Lion's tail, was observed to be westward of the
meridian, and to have 40 deg. of altitude : what hour was
it, and what was the star's azimuth ?

Answer. By turning the globe westward on its axis till the star
cuts 40 deg. of the quadrant west of the meridian, the index will have
passed over 20 hours ; consequently, the star has 40 deg. of altitude
west of the meridian, 20 hours from noon, or at eight o'clock in the
morning. Its azimuth will be 62§ deg. from the south towards the
west.

3. At London, on the 1st of September, the altitude of
Benetnach in Ursa Major, marked -/?, was observed to be
36 degrees above the horizon, and west of the meridian ;
what hour was it, and what was the star's azimuth ?

4. On the 21st of December, the altitude of Sirius,
when west of the meridian at London, was observed
to be 8 deg. above the horizon ; what hour was it, and
what was the star's azimuth ?

5. On the 12th of August, Menkar in the Whale's jaw,
marked a, was observed to be 37 deg. above the horizon
of London, and eastward of the meridian ; what hour was
it, and what was the star's azimuth ?

both sides of it. Any star may be taken at bleasure, but it is best to
take one not too near the meridian, because for some time before the
star comes to the meridian, and after it has passed it, the altitude varies
very little.

314- PROBLEMS PERFORMED BY Part ILL

PROBLEM LXXXVI.

Given the latitude of a place, day of the month, and hour of
the day, to find the altitude of any star, and its azimuth.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and screw
the quadrant of altitude upon the brass meridian over that
latitude ; find the sun's place in the ecliptic, bring it to
the brass meridian, and set the index of the hour-circle
to 12 ; then, if the given time be before noon ; turn the
globe eastward on its axis till the index has passed over
as many hours as the time wants of noon ; if the time
be past noon, turn the globe westward till the index has
passed over as many hours as the time is past noon : let
the globe rest in this position, and move the quadrant of
altitude till its graduated edge coincides with the centre
of the given star,; the degrees on the quadrant, from the
horizon to the star, will be the altitude ; and the distance
from the north or south point of the horizon to the qua-
drant, counted on the horizon, will be the azimuth from
the north or south.

EXAMPLES. 1. What are the altitude and azimuth of
Capella at Rome, when it is five o'clock in the morning
on the 2d of December ?

Answer. The altitude is 41 deg. 58 min., and the azimuth 60 deg.
50 min. from the north towards the west.

2. Required the altitude and azimuth of Altair in
Aquila on the 6th of October, at nine o'clock in the
evening, at London ?

3. On what point of the compass does the star Alde-
baran bear at the Cape of Good Hope, on the 5th of
March, at a quarter past eight o'clock in the evening ; and
what is its altitude?

4. Required the altitude and azimuth of Acyone in the
Pleiades marked rt, on the 21st of December, at four
o'clock in the morning, at London ?

Chap. II. THE CELESTIAL GLOBE. ' 315

PROBLEM LXXXVII.

Given the latitude of the place, day of ike month, and
azimuth of a star, to find the hour of the night and the
stars altitude.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and screw
the quadrant of altitude upon the brass meridian over that
latitude ; find the sun's place in the ecliptic, bring it to
the brass meridian, and set the index of the hour-circle to
] 2 ; bring the lower end of the quadrant of altitude to
coincide with the given azimuth on the horizon, and
hold it in that position ; turn the globe westward till the
given star conies to the graduated edge of the quadrant,
and the hours passed over by the index will be the time
from noon ; the degrees on the quadrant, reckoning from
the horizon to the star, will be the altitude.

EXAMPLES. 1. At London, on the 28th of December,
the azimuth of Deneb in the Lion's tail marked /3, was
62£ deg. from the south towards the west ; what hour was
it, and what was the star's altitude ?

Ansiver. By turning the globe westward on its axis, the index will
pass over 20 hours before the star intersects the quadrant ; therefore
the time will be 20 hours from noon, or eight o'clock in the morning ;
and the star's altitude will be 40 deg.

2. At London, on the 5th of May, the azimuth of Cor
Leonis, or Regulus, marked «, was 74 deg. from the south
towards the west ; required the star's altitude, and the
hour of the night ?

3. On the 8th of October, the azimuth of the star
marked ft, in the shoulder of Auriga, was 50 deg. from
the north towards the east ; required its altitude at Lon-
don, and the hour of the night ?

4. On the 10th of September, the azimuth of the star
marked c, in the Dolphin, was 20 deg. from the south
towards the east ; required its altitude at London, and the
hour of the night ?

p 2

316 PROBLEMS PERFORMED BY Part III.

PROBLEM LXXXVIII.

Two stars being given, tfie one on the meridian, and the
other on the east or west part of the horizon, to find the
latitude of the place.

RULE. Bring the star which was observed to be on the
meridian, to the brass meridian; keep the globe from
turning on its axis, and elevate or depress the pole till the
other star comes to the eastern or western part of the
horizon ; then the degrees from the elevated pole to the
horizon will be the latitude.

EXAMPLES. 1. When the two pointers* of the Great
Bear, marked a and j3, or Dubhe and /3, were on the me-
ridian, I observed Vega in Lyra to be rising ; required
the latitude ?

Answer. 27 deg. north.

2. When Arcturus in Bootes was on the meridian,
Altair in the Eagle was rising; required the latitude?

3. When the star marked j3 in Gemini was on the me-
ridian, s in the shoulder of Andromeda was setting ; re-
quired the latitude?

4-. In what latitude are a and /3, or Sirius and $ in Canis
Major rising, when Algenib, or a, in Perseus, is on the
meridian ?

PROBLEM LXXXIX.

The latitude of the place, the day of the month, and two
stars that have the same azimuth \, being given, to find
the hour of the night.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and

* These two stars are called the pointers, because a line drawn
through them, points to the polar star in UrsaJVlinor. See page 131.

f To find what stars have the same azimuth. — Let a smooth rect
angular board of abo*ut a foot in breadth, and three feet high (or of

Chap. II. THE CELESTIAL GLOBE. 317

ecrew the quadrant of altitude upon the brass meridian
over that latitude ; find the sun's place in the ecliptic, bring
it to the brass meridian, and set the index of the hour-
circle to 12; turn the globe on its axis from east to west
till the two given stars coincide with the graduated edge of
the quadrant of altitude ; the hours passed over by the
index will shew the time from noon; and the common
azimuth of the two stars will be found on the horizon.

EXAMPLES. 1. At what hour, at London, on the 1st
of May, will Altair in the Eagle, and Vega in the Harp,
have the same azimuth, and what will tha,t azimuth be ?

Answer. By bringing the sun's place to the meridian, &c. and
turning the globe westward, the index will pass over 15 hours before
the stars coincide with the quadrant : hence they will have the same
azimuth at 1 5 hours from noon, or at three o'clock in the morning ;
and the azimuth will be 42i deg. from the south towards the east.

2. On the 10th of September, what is the hour at
London, when Deneb in Cygnus, and Markab in Pegasus,
have the same azimuth, and what is the azimuth ?

3. At what hour on the 15th of April will Arcturus and
Spica Virginis have the same azimuth at London, and
what will that azimuth be ?

4. On the 20th of February, what is the hour at
Edinburgh when Capella and the Pleiades have the same
azimuth, and what is the azimuth ?

5. On the 21st of December, what is the hour at Dub-
lin when « or Algenib in Perseus, and $ in the Bull's
horn, have the same azimuth, and what is the azimuth ?

any height you please), be fixed perpendicularly upon a stand ; draw
a straight line through the middle of the board, parallel to the sides :
fix a pin in the upper part of this line, and make a hole in the board at
the lower part of the line ; hang a thread with a plummet fixed to it
upon the pin, and let the ball of the plummet move freely in the hole
made in the lower part of the board : set this board upon a table in a
window, or in the open air, and wait till the plummet ceases to vibrate ;
then look along the face of the board, and those stars which are partly
hid from your view by the thread will have the same azimuth.

P 3

318 PROBLEMS PERFORMED BY Part III.

PROBLEM XC.

The latitude of ike place, the day of the month, and two
stars that have the same altitude, being given, to find the
hour of the night.

EXAMPLES. 1. At what hour at London, on the 2d
of September, will Markab in Pegasus, and a in the head
of Andromeda, have each 30 deg. of altitude ?

Answer. At a quarter past eight in the evening.

2. At what hour at London, on the 5th of January,
will «, Menkar, in the Whale's jaw, and a, Aldebaran, in
Taurus, have each 35 deg. of altitude ?

3. At what hour at Edinburgh, on the 10th of Novem-
ber, will «, Altair, in the body of the Eagle, and £, in the
tail of the Eagle, have each 35 deg. of altitude ?

4. At what hour at Dublin, on the 15th of May, will »?,
Benetnach, in the Great Bear's tail, and y, in the shoulder
of Bootes, have 56 deg of altitude ?

PROBLEM XCL

The altitudes of two stars having the same azimuth, and
that azimuth being given, to find the latitude of the place.

RULE. Place the graduated edge of the quadrant of
altitude over the two stars, so that each star may be
exactly under its given altitude on the quadrant ; hold the
quadrant in this position, and elevate or depress the pole
till the division marked o, on the lower end of the qua-
drant, coincides with the given azimuth on the horizon :

Chap. II. THE CELESTIAL GLOBE. 3} 9

when this is effected, the elevation of the pole will be the
latitude.

EXAMPLES. 1. The altitude of Arcturus was observed
to be 40 deg., and that of Cor. Caroli 68 deg. ; their com-
mon azimuth at the same time was 71 deg. from the south
towards the east ; required the latitude ?

Answer. 51 £ deg. north.

2. The altitude of E in Castor was observed to be 40
deg., and that of /3 in Procyon 20 deg. ; their common
azimuth at the same time was 73£ deg. from the south to-
wards the east ; required the latitude ?

3. The altitude of a, Dubhe, was observed to be 40
deg., and that of y in the back of the Great Bear 29| deg.,
their common azimuth at the same time was 30 deg. from
the north towards the east ; required the latitude ?

4. The altitude of Vega, or a in Lyra, was observed to
be 70 deg., and that of a in the head of Hercules 39£
deg., their common azimuth at the same time was 60 deg.
from the south towards the west ; required the latitude ?

PROBLEM XCII.

The day of the month being given, and the hour when any
known star rises or sets, to find the latitude of the, place.

RULE. Find the sun's place in the ecliptic, bring it to
the brass meridian, and set the index of the hour-circle
to 12; then, if the given time be before noon, turn the
globe eastward till the index has passed over as many
hours as the time wants of noon ; but, if the given time
be past noon, turn the globe westward till the index has
passed over as many hours as the time is past noon ; ele-
vate or depress the pole till the centre of the given star
coincides with the horizon ; then the elevation of the pole
will shew the latitude.

EXAMPLES. 1. In what latitude does c, Mirach, in
Bootes, rise at half past twelve o'clock at night, on the
tenth of December ?

Answer. 5l£ deg. north.

p 4

320 PROBLEMS PERFORMED BY Part III.

2. In what latitude does Cor Leonis, or Regulus, rise
at ten o'clock at night, on the 21st of January ?

3. In what latitude does j3, Rigel in Orion, set at four
o'clock in the morning, on the 21st of December?

4. In what latitude does j9, Capricornus, set at eleven
o'clock at night, on the 10th of October?

PROBLEM XCIII.

To find on what day of the year any given star passes the
meridian at any given hour.

RULE. Bring the given star to the brass meridian, and
set the index to 12; then, if the given time be before
noon *, turn the globe westward till the index has passed
over as many hours as the time wants of noon ; but, if the
given time be past noon, turn the globe eastward till the
index has passed over as many hours as the time is past
noon ; observe that degree of the ecliptic which is inter-
sected by the graduated edge of the brass meridian, and
the day of the month answering thereto, on the horizon,
will be the day required.

EXAMPLES. I. On what day of the month does Pro-
cyon come to the meridian of London at three o'clock in
the morning ?

Answer. Here the time is nine hours before noon ; the globe must
therefore be turned nine hours towards the west, the point of the eclip-
tic intersected by the brass meridian will then be the ninth of f , an-
swering nearly to the first of December.

2. On what day of the month, and in what month, does
«, Alderarnin, in Cepheus, come to the meridian of Edin-
burgh at ten o'clock at night ?

Answer. Here the time is ten hours after noon ; the globe must
therefore be turned ten hours towards the east, the point of the ecliptic
intersected by the brass meridian will then be the 17th of njj, answer-
ing to the ninth of September.

* If the given star comes to the meridian at noon, the sun's place
will be found under the brass meridian, without turning the globe ; if
the given star comes to the meridian at midnight, the globe may be
turned either eastward or westward till the index has passed over twelve
hours.

Ckap.ll. THE CELESTIAL GLOBE. 321

3. On what day of the month, and in what month, does
0, Deneb, in the Lion's tail, come to the meridian of Dub-
lin at nine o'clock at night ?

4. On what day of the month, and in what month, does
Arcturus in Bootes come to the meridian of London at
noon?

5. On what day of the month, and in what month, does
8 in the Great Bear come to the meridian of London at
midnight ?

6. On what day of the month, and in what month, does
Aldebaran come to the meridian of Philadelphia at five
o'clock in the morning at London ?

PROBLEM XCIV.

The day of the month being given, to find at what hour any
given star comes to the meridian. *

RULE. Find the sun's place in the ecliptic, bring it to the
brass meridian, and set the index of the hour-circle to 12;
turn the globe westward on its axis till the given star comes
to the brass meridian, and the hours passed over by the
index will be the time from noon when the star culminates.

OR, WITHOUT THE GLOBE.

Subtract the right ascension of the sun for the given
day from the right ascension of the star, and the remain-
der will be the time of the star's culminating nearly. f —

* This problem is comprehended in Problem LXXI.

t The time of any particular star's culminating, or passing the meri-
dian of any place, depending entirely on its distance east or west from
the sun, it follows that, on any given day, the same stars must culmi-
nate nearly at the same hour, according to the reckoning of time at
any other place. Thus, suppose that any given star culminates at
noon at any given place, then the time from noon at which it will
culminate on that day, at any other place, cannot exceed about 4 m»-
nntes, that being the mean daily variation of the sun's right ascension.
We may, therefore, say, without any considerable error, that on any
given day any proposed star culminates at one and the same time of
P 5

322 PROBLEMS PERFORMED BY Part 111 t

If the sun's right ascension exceeds the star's, add 24-
hours to the star's before you subtract.

EXAMPLES. I. At what hour does Cor Leonis, or
Regulus, come to the meridian of London on the 23d of
September ?

Answer. The index will pass over 21| hours ; hence this star cul-
minates, or comes to the meridian, 21 f hours after noon, or at three
quarters past nine o'clock in the morning.

2. At what hour does Arcturus come to the meridian
of London on the 9th of February ?

Answer. The index will pass over 16| hours ; hence Arcturus
culminates 16§ hours after noon, or at half past four o'clock in the
morning.

3. Required the hours at which the following stars come to
the meridian of London on the respective days annexed : —

Bellatrix, January 9th.
Menkar, May 18th.
Etanin, Sept. 22d.
a Dubhe, Dec. 20th.

P Mirach, October 5th.
Aldebaran, Feb. 12th.
jS Aries, November 5th.
)3 Taurus, January 24th.

4. At what time will Sirius come to the meridian of
Greenwich on the 18th of December, 184-5, his right as-
cension being 6h 38'*, and the sun's right ascension 17h
45' ?t

the day on every part of the globe. If, however, great exactness be
required, in order to find the time of any given star's culminating for
any other meridian than that of Greenwich, first find the true time of its
culminating at Greenwich, and then allow 10 seconds of time for
every 15° of longitude ; which subtract from the time at Greenwich, for
places in west longitude, or add to that time for places in east longi-
tude ; and the result will show the time of the star's culminating at the
proposed meridian.

It is obvious, that this degree of nicety is not to be attained by the
globe ; but the right ascension and declination of 100 principal fixed
stars for 1 845, together with their annual variation being given in the
Nautical Almanac for that year, the time of their culminating on any day,
for any other meridian than that of Greenwich, and also for any other
year, may be found by the method here given with the greatest accuracy.

* See page 436 of the Nautical Almanac.

t See Nautical Almanac, page II of the month.

Chap. II. THE CELESTIAL GLOBE. 323

PROBLEM XCV.

Given the azimuth of a known star, the latitude, and the
hour, to find the stars altitude, and the day of the month.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the given place,
screw the quadrant of altitude upon the brass meridian
over that latitude, bring the division marked o on the
lower end of the quadrant to the given azimuth on the
horizon, turn the globe till the star coincides with the
graduated edge of the quadrant, and set the index of the
hour-circle to 12 ; then, if the given time be before noon,
turn the globe westward till the index has passed over as
many hours as the time wants of noon ; if the given time be
past noon, turn the globe eastward till the index has passed
over as many hours as the time is past noon ; observe that
degree of the ecliptic which is intersected by the graduated
edge of the brass meridian, and the day of the month an-
swering thereto, on the horizon, will be the day required.

EXAMPLES. 1. At London, at ten o'clock at night, the
azimuth of Spica Virginis was observed to be 40 deg. from
the south towards the west ; required its altitude, and the
day of the month ?

Answer. The star's altitude is 20 deg., and the day is the 18th of
June. The time being ten hours past noon, the globe must be turned
ten hours towards the east.

2. At London, at four o'clock in the morning, the
azimuth of Arcturus was 70 deg. from the south towards
the west ; required its altitude, and the day of the month ?

Answer. Here the time wants eight hours of noon, therefore the
globe must be turned eight hours westward ; the altitude of the star
will be found to be 40 deg., and the day the 12th of April.

3. At Edinburgh, at eleven o'clock at night, the azi-
muth of a Serpentarius, or Ras Alhagus, was 60 deg. from
the south towards the east ; required its altitude, and the
day of the month ?

4t. At Dublin, at two o'clock in the morning, the azi-

324- PROBLEMS PERFORMED BY Part III.

muth of 0 Pegasi, or Scheat, was 70 deg. from the north
towards the east ; required its altitude, and the day of the
month ?

PROBLEM XCVI.

The altitudes of two stars being given, to find the latitude
of the place.

RULE. Subtract each star's altitude from 90 degrees ;
take successively the extent of the number of degrees,
contained in each of the remainders, from the equinoctial,
with a pair of compasses ; with the compasses thus ex-
tended, place one foot successively in the centre of each
star, and describe arcs on the globe with a black-lead
pencil; these arcs will cross each other in the zenith;
bring the point of intersection to that. part of the brass
meridian which is numbered from the equinoctial towards
the poles, and the degree al?ove it will be the latitude.

EXAMPLES. 1. At sea, in north latitude, I observed
the altitude of Capella to be 30 deg., and that of Alde-
baran 35 deg. ; what latitude was I in ?

Answer. With an extent of 60 deg. ( = 90° — 30°) taken from the
equinoctial, and one foot of the compasses in the centre of Capella,
describe an arc towards the north ; then with 55 deg. ( = 90°— 35°),
taken in a similar manner, and one foot of the compasses in the centre
of Aldebaran, describe another arc, crossing the former ; the point of
intersection brought to the brass meridian will show the latitude to be
20§ deg. north.

2. The altitude of Markab in Pegasus was 30 deg., and
that of Altaif in the Eagle, at the same time, was 65 deg. ;
what was the latitude, supposing it to be north ?

3. In north latitude the altitude of Arcturus was ob-
served to be 60 deg., and that of $ or Deneb, in the
Lion's tail, at the same time, was 70 deg. ; what was the
latitude ?

4. In north latitude, the altitude of Procyon was ob-
served to be 50 deg., and that of Betelgeux in Orion, at
the same time, was 58 deg. ; required the latitude of the
place of observation ?

THE CELESTIAL GLOBE. 325

PROBLEM XCVII.

The meridian altitude of a known star being given at any
place in north latitude, to find the latitude.

RULE. Bring the given star to that part of the brass
meridian which is numbered from the equinoctial towards
the poles; count the number of degrees in the given alti-
tude on the brass meridian from the star towards the south
part of the horizon, and mark where the reckoning ends ;
elevate or depress the pole till this mark coincides with
the south point of the horizon, and the elevation of the
north pole above the north point of the horizon will show
the latitude.

EXAMPLES. 1. In what degree of north latitude is the
meridian altitude of Aldebaran 52^ deg. ?

Answer. 53 deg. 36 min. north.

2. In what degree of north latitude is the meridian
altitude of 0, one of the pointers in Ursa Major, 90 deg. ?

3. In what degree of north latitude is y, in the head of
Draco, vertical when it culminates ?

4. In what degree of north latitude is the meridian al-
titude of e or Mirach in Bootes, 68 deg.?

PROBLEM XCVIII.

The latitude of a place, day of the month, and hour of the
day, being given, to find the NONAGESIMAL DEGREE *
of the ecliptic, its altitude and azimuth, and the MEDIUM
CCELI.

RULE. Elevate the north pole to the latitude of the
given place, and screw the quadrant of altitude upon the

* The nonagesimal degree of the ecliptic is that point which is the
most elevated above the horizon, and is measured by the angle which
the ecliptic makes with the horizon at any elevation of the pole ; or, it
is the distance beneath the zenith of the place and the pole of the eclip-
tic. This angle is frequently used in the calculation of solar eclipses.
The medium coeli, or mid-heaven, is that point of the ecliptic which
is upon the meridian.

326 PROBLEMS PERFORMED BY Part III.

brass meridian over that latitude ; find the sun's place in
the ecliptic, bring it to the brass meridian, and set the in-
dex of the hour-circle to 12; then, if the given time be
before noon, turn the globe eastward till the index has
passed over as many hours as the time wants of noon ;
but, if the given time be past noon, turn the globe west-
ward till the index has passed over as many hours as the
time is past noon, and fix the globe in this position ; count
90 deg. upon the ecliptic from the horizon (either eastward
or westward), and mark where the reckoning ends, for
that point of the ecliptic will be the nonagesimal degree,
and the degree of the ecliptic cut by the brass meridian,
will be the medium coeli ; bring the graduated edge of the
quadrant of altitude to coincide with the nonagesimal de-
gree of the ecliptic thus found, and the number of de-
grees on the quadrant, counted from the horizon, will be
the altitude of the nonagesimal degree ; the azimuth will
be seen on the horizon.

EXAMPLES. 1. On the 21st of June, at forty -five
minutes past three o'clock in the afternoon, at London,
required the point of the ecliptic which is the nonagesi-
mal degree, its altitude and azimuth, the longitude of the
medium cceli, and its altitude, &c. ?

Answer. The nonagesimal degree is 10 deg. in Leo, its altitude is
54 deg., and its azimuth 22 deg. from the south towards the west, or
nearly S.S.W. The mid-heaven, or point of the ecliptic under the
brass meridian, is 24 deg. in Leo, and its altitude above the horizon
is 52 deg. The degree of the equinoctial cut by the brass meridian,
reckoning from the point Aries, is the right ascension of the mid-
heaven, which in this example is 146 deg. The rising point of the
ecliptic will be found to be 10 deg. in Scorpio, and the setting point
10 deg. in Taurus. If the graduated edge of the quadrant be brought
to coincide with the sun's place, the sun's altitude will be found to be
39 deg. and his azimuth 78 § deg. from the south towards the west, or
nearly W. by S.

2. At London, on the 24th of April, at nine o'clock
in the morning ; required the point of the ecliptic which
is the nonagesimal degree, its altitude and azimuth, the
point of the ecliptic which is the mid-heaven, &c. &c. ?

3. At Limerick, in 52 deg. 22 min. north latitude, on
the 15th of October, at five o'clock in the afternoon; re.

Chap. II. THE CELESTIAL GLOBE. 327

quired the point of the ecliptic which is the nonagesimal
degree, its altitude and azimuth, the point of the ecliptic
which is the mid-heaven, &c. &c. ?

4-. At Dublin, in latitude 53 deg. 21 min. north, on the
15th of January, at two o'clock in the afternoon; required
the longitude, altitude, and azimuth, of the nonagesimal
degree ; and the longitude and altitude of the medium
coeli, &c. &c. ?

PROBLEM XCIX.

The latitude of a place, day of the month, and the hour,
together with the altitude and azimuth of a star, being
given} to find the star.

RULE. Elevate the pole so many degrees above the
horizon as are equal to the latitude of the place, and
screw the quadrant of altitude on the brass meridian
over that latitude ; find the sun's place in the ecliptic,
bring it to the brass meridian, and set the index of the
hour-circle to 12; then, if the given time be before
noon, turn the globe eastward till the index has passed
over as many hours as the time wants of noon ; but, if
the time be past noon, turn the globe westward till the
index has passed over as many hours as the time is past
noon ; let the globe rest in this position, and bring the
division marked O on the quadrant to the given azimuth
on the horizon ; then, immediately under the given alti-
tude on the graduated edge of the quadrant, you will find
the star.

EXAMPLES. 1. At London, on the 21st of December,
at four o'clock in the morning, the altitude of a star was
50 deg., and its azimuth was 37 deg. from the south to-
wards the east ; required the name of the star ?

Answer. Deneb, or & in the Lion's tail.

2. The altitude of a star was 27 deg., its azimuth 76£
deg. from the south towards the west, at eleven o'clock
in the evening, at London, on the llth of May; what star
was it?

3. At London, on the 2 1st of December, at four o'clock

328 PROBLEMS PERFORMED BY. Part III.

in the morning, the altitude of a star was 8 deg., and its
azimuth 51 deg. from the south towards the west ; required
the name of the star?

4. At London, on the 1st of September, at ninpo'cWk
in the evening, the altitude of a star was 47 deg., and its
azimuth 73 deg. from the south towards the east ; required
the name of the star ?

PROBLEM C.*

To find very correctly, by the globe, the time of the moons
culminating, or coming to the meridian, on any given day.

RULE. Find the moon's right ascension and declination
at noon by the Nautical Almanac, and mark its place on
the globe. Also find the sun's place in the ecliptic for the
given day ; bring it to the meridian, and set the index to
12; turn the globe westward on its axis, till the moon's
place comes to the meridian, and note the number
of hours passed over by the index. Then find in the
Nautical Almanac the moon's right ascension and declin-
ation at this time, and bring that point to the meridian ;
the number of hours from noon, now shown by the index,
will be very nearly the true time of the moon's passing
the meridian.

OR, WITHOUT THE GLOBE.

Find the moon's age by the table, at page 184-., which
multiply by -82 f, and cut off two figures from the right
hand of the product ; the left-hand figures will be the
hours ; the right-hand figures must be multiplied by 60,
for minutes.

EXAMPLES. 1. At what hour, on the 14th of January,
1845, will the moon pass the meridian of Greenwich, the
moon's right ascension at noon being 0 hrs. 47 min., and
declination 9° 15'N.?

By the Globe. The point of the moon's declination at

* This problem is substituted by the editor for the very incorrect
one given in former editions.

f For, the synodic revolution of the moon being about 29£ days, we
have, by the rule of three, as 29^ d. I 24 h. : : 1 d. : -82 h. nearly.

Chap. II. THE CELESTIAL GLOBE. 329

noon comes to the meridian at about 10 min. past 5 o'clock
in the afternoon ; at which time, by page VII. of the month
in the Nautical Almanac for 1845, the moon's right as-
cension will be 0 hr. 57 min. ; bringing this last to the me-
ridian, it will be found that the time from noon is 5 hrs.
20 min. (as nearly as can be read off .on a globe), and
agrees within about 1 min. of the time of the moon's passage
given in page IV. of the month in the Nautical Almanac.
By the Table (page 184-.). The moon's age is 6, or more
nearly 6^, which multiplied by *82 gives 5'33, that is, 5 hrs.
and *33 over; this multiplied by 60 produces nearly 19
minutes. Hence, by this method, the moon culminates at
5 hrs. 19 min. in the afternoon, nearly as given in the
Nautical Almanac, which is 5 hrs. 21*3 min.

2. At what hour, on the 13th of March, 1845, will the
moon pass over the meridian at Greenwich, the moon's
right ascension at noon being 3 hrs. 29 min., and declin-
ation 19 deg. 13 min. N.?

3. At what hour, on the 1st of January } 1846, will the
moon pass over the meridian of Greenwich, the moon's
right ascension at noon being 22 hrs. 4 min., and declin-
ation 6 deg. 39 min. S. ?

PROBLEM CI.

The day of the month, and time of high water at the full
arid change of the moon being given, to find the time of
high water on the given day at anyplace within the limits
of the table.

RULE. Find the time at which the moon comes to the
meridian of the given place by the preceding problem, to
which add the time of high water at the given place at
the full and change of the moon (taken from the follow-
ing Table), and the sum will show the time of high water
in the afternoon. If the sum exceed 1 2 hours, subtract
12 hours and 24 minutes from it, and the remainder will
show the time of high water in the morning ; but if the
sum exceed 24 hours, subtract 24 hours and 48 minutes
from it, and the remainder will show the time of high water
in the afternoon.

330 PROBLEMS PEREORMED BY Part III.

OR, BY THE TABLE, PAGE 184.

Find the moon's age by the Table, at page 184-., and
take out the time from the right-hand column thereof
answering to the moon's age ; to which add the time of
high water at the full and change of the moon (taken from
the following Table), and the sum will show the time of
high water in the afternoon. If the sum exceed 12 hours,
subtract 12 hours and 24- minutes from it, and the re-
mainder will show the time of high water in the morning ;
but if the sum exceed 24 hours, subtract 24 hours and
48 minutes from it, and the remainder will show the time
of high water in the afternoon.

OR THUS:

Find the time of the moon's coming to the meridian of
Greenwich on the given day, at page IV. of the month in
the Nautical Almanac ; take out the correction (from the
following Table, page 332.) to correspond to this time, and
apply it as the Table directs ; to the result add the time of
high water at the full and change of the moon (taken from
the following table), and the sum will show the time of
high water in the afternoon. If the sum exceed 12 or 24
hours, proceed as above.

EXAMPLES. 1. Required the time of high water at
London Bridge on the 29th of April, 1844, the moon's
right ascension at noon being 11 hrs. 35 min., and her de-
clination 2 deg. 50 min. south ?

Answer, By the Globe. The moon comes to the meridian at 9Ti . 24m.
Time of high water at the full and change at London - 2 7

Time of high water in the afternoon - j -. 11 31

By the Table, page 184. The moon's age is 12, the time answering
to which, in Table, p. 185. - ' -. 1O h. 9 m.

Time of high water at the full and change 2 7

Time of high water at 16 min. past 12 at night - 12 16

Chap. II. THE CELESTIAL GLOBE. 33J

By the Nautical Almanac, — The moon comes to the me- 1

ridianat - - ) 9h' 24m-

The time from the right-hand Table following, answer- "I
ing to 9 hours 24 rain., is - - - J

Sum - - 9 47

Time of high water at London at the full and change 2 7

Time of high water 54 min. after 1 1 at night.* 1 1 54

2. Required the time of high water at London, on the
9th of Febuary, 184-4, the moon's right ascension at noon
being 13 hrs. 35 min., and her declination 14? deg. 20 min.
south ?

3. Required the time of high water at Aberdeen, on
the 9th of February, 1844, the moon's right ascension at
noon being 13 hrs. 35 min., and her declination 14 deg.
20 min. south ?

4. Required the time of high water at Liverpool Dock
on the 14th of August, 1845 ? By the Nautical Almanac
the moon comes to the meridian of Greenwich at 9 hrs
29 min.

5. Required the time of high water at Bristol, on the
2d of September, 1845, the moon's right ascension at
noon being 11 hrs. 5 min., and her declination 1 deg.
6 min. north?

6. Required the time of high water at Dublin, on the
1st of January, 1846, the moon's right ascension at noon
being 22 hrs. 4 min., and her declination 6 deg. 38 min.
south ?

* Here are three methods of performing the same problem, and the
results all differ from each other : the first is nearest to the time given
in the Nautical Almanac for 1844, p. 546. ; which is 11 h. 36 min.
For ascertaining the time of high water more accurately, see an Ele-
mentary Treatise on the Tides by Sir J. Lubbock, published in 1839.

332

PROBLEMS PERFORMED BY

Part III

A TABLE

Of the Time of High Water at NEW and FULL MOON
at the principal Places in the British Islands.*

1 § T3
O "j*

i'S »

1* *w;
CH ^

Correction to be sub-
tracted or added.

Aberdeen iMl^

Fifeness 2'1 0"

Aberystwith . ... 7 30

Flamborough Head 4 30
North Foreland.... 11 20
South Foreland 11 20
Foulness, .. 6 45

Aldborough 10 45

St. Andrew's 2 0
Arran Island 11 15

Bamborough 3 30
Banff 0 41

Fowey 5 30

2
3
4
5
6
7

Sub.
0 0
0 1
0 34
0 50
1 3
1 9
1 3
1 35

GalwayBay 4 30
Fort George ...11 40

Beachy Head 11 50
St Bee's Head .10 45

Gravesend 1 SO

Belfast 10 5

Greenock ... 1 1 45

Bembridge Point... 10 15
Berwick 2 18

Hartland Point 4 30
Hartlepool. ... 3 45

Boston 7 15

Harwich 11 30

St. Bride's Bay 6 0

Holyhead 10 0

Hull 6 0

Bridport 6 0

Kinsale ' 4 30

Brighton 11 38

Leith 2 22

Bristol . 7 15

Limerick 4 30

Caithness Point 9 0
Cantire, Mull 6 0
Cape Clear 40

Liverpool Dock.... 11 22
London Bridge 2 7
Milford ... . 5 45

8
9
10
11
12

Add
0 2
0 23
0 24
0 14
0 0

Cork Harbour 4 30
Cowes 10 45

Newcastle 4 0

Orfordness 10 4

Cromartie 11 45

Plymouth 5 33

Cromer 7 0

Port Patrick 11 0
Portland 6 15

Cullen 0 0

Dartmouth 6 5
Dingle Bay 3 30

Portsmouth Dock.. 11 40
Ramsgate Harbour 1 1 20
Rochester 0 45

13
14
15
16
17
18
19

21 ,
22 !
23 !
24 |

Sub.
0 17
0 34
0 50
1 3
1 9
1 3
0 35

Add
0 2
0 23
0 24
0 14
0 0

Dover... 11 10

Dublin Bar 11 12

Sandwich 11 30

Dunbar... 2 20

Scarborough . 4 25

Dunbarlon 11 15

Sli^o Bay 5 59

Dundee... . 2 35

Southampton 11 40
Stockton... ... 3 30

Dungeness 10 50

Eddystone 5 15

Tynemouth ... 2 50

Edinburgh 2 20

Torbay 6 5

Exeter 10 30

Exmouth Bar 6 25
Falmouth 5 15

Whitby 3 45

Whitehaven 11 15

Yarmouth Road.... 8 40

Corrected from the Nautical Almanac for 1845

Chap. II. THE CELESTIAL GLOBE. 333

PROBLEM CII.

To describe the apparent path of any planet^ or cornet^ among
the fixed stars.

RULE. Draw a straight line, E Q, Plate V., to represent
the equinoctial, from any fixed point, as at y ; divide it into
any number of equal parts, as I, II, III, IV, &c., to repre-
sent hours of right ascension ; these again may be divided
into 15 degrees each, then each degree will correspond
to 4 minutes of time. Parallel with E Q, at convenient
distances, draw the lines A B, C D, and divide them in
a similar manner to the equinotcial. At right angles to
these draw A C, B D, and divide them into degrees and
half degrees of declination.* Through the point Aries,
and nearly at an angle of 23-J- degrees with the equator,
draw £ C, the ecliptic, to represent the sun's path, cor-
responding to the days of the month. The ecliptic may
be described, and the longitudes laid down sufficiently near,
by taking the sun's right ascension and declination from the
Nautical Almanac for every day, and marking the dates.
The longitude for the respective days will be found in
page III. of each month of the Nautical Almanac, and may
be set off in correspondence with the days of the month.

EXAMPLE. Delineate the path of the planet Jupiter
from the 1st of December, 1844, to the 31st of Decem-
ber, 1846; the right ascensions and declinations being
as follows :

December 1st, 1844, right ascension 23 hrs. 4-1 m. ;
and declination 3° 33' S.

1845.

Right Asc.

Declin.

1846. Right Asc.

Declin.

Jan.

23h

52m

2°

19'

57m

10°

Feb.

March 1

. 0

April

May

June

July

* These should, strictly speaking, be drawn from a scale of Tan-
gents, but for popular purposes, and within 30 or 40 degrees from th«
equinoctial, equal distances will be sufficient to exhibit portions of tl
heavens on a small scale.

334 PROBLEMS PERFORMED BY Part III.

1845. Right Asc. Declin.

Aug.
Sept.
Oct.
Nov.
Dec.

2h 30» 13° 27' N.

2 35 3 47 N.

2 29 3 12 N.

2 14 1 56 N.

21 0 51 N.

1846. Right Asc. Declin.

4°36m 21°18'N.

4 54 21 50 N.

52 22 0 N.

4 57 21 53 N.

4 42 21 29 N.

As Jupiter performs his revolution in 11 years 317
days 1 4 h. 2m. 8'5 s., he will have nearly the same posi-
tions in the years 1866, 1867, and 1868.

Jupiter's path, when delineated, will be south of the
ecliptic in the order of the letters A, B, C, D, E, F, G,
&c. Thus he will appear at A on the 1 st of December,
1844; at B on the 1st of January, 1845; at C on the 1st
of February, at E on the 1st of April, at G on the 1st
of June, and at H on the 1st of July ; when he arrives at
J, which will happen on the 1st of September, 1845, he
will apparently retrograde, by returning again nearly to
G (almost in his former path), where he will be situated
on the 1st of January, 1846. He will then begin to ad-
vance again towards J, and will arrive at K on the 1st of
April, 1846; on the 1st of June of the same year he will
arrive at M, and on the 1st of October at Q, where he
will apparentlv remain stationary for a short time, and
then retrograde towards O. When Jupiter is near the
sun's place, as in the months of March and April, he will
not be visible, in consequence of the light of the sun.

In the same manner the places and situations of the
fixed stars may be delineated, by taking their right ascen-
sions and declinations from a globe *, or more accurately
from a catalogue of stars, such as the one published by the
Royal Astronomical Society of London. Thus Aldebaran^
the principal star in the constellation Taurus, will be found
by the globe, or in the catalogue, to be situated in 4 b.
26 m. Rt. asc., and 16° 10' N. declination ; therefore, by

* It is necessary to remind the young student that the stars appear
in a contrary order in the heavens from what they do on the surface
of a globe. In the heavens we see the concave part, on the globe the
convex ; therefore it is necessary to conceive the eye to be in the
centre of the celestial globe, in order to refer the stars on it to their
right places in the heavens.

Delineations of the stars will enable the young student to know
their names and places sooner than by a globe.

Part IV. THE CELESTIAL GLOBE. 335

taking a ruler, and drawing a line from 4 h. 26 m. on the
south side of the equinoctial to 4 h. 26 m. on the north side,
or vice versa, and from 16° 10' of north declination on the
left side of the map to the same declination on the right,
the point where the two lines cross will be the place of
that star. The places of other stars may be depicted in a
similar manner.

The constellations Orion and Taurus, which are exhi-
bited on the left-hand side of the map (Plate V.), are very
conspicuous objects in the southern part of the heavens
during the latter part of December and the months of
January and February, about 9 or 10 o'clock in the even-
ing.— Orion serves as an excellent guide for determining
the positions of several other constellations, particularly of
Canis Major, which may be seen a little lower down towards
the left ; Canis Minor about a sign or 30° to the east ;
Auriga will be seen on the north, &c. See page 125.

PART IV. CONTAINS

I. A promiscuous Collection of Examples for Exercise on the
Globes. — 2. A Collection of Questions, with References to
the Pages where the Answers will be found ; designed as
an Assistant to the Tutor in theExamination of his Pupils.

CHAPTER I.
Promiscuous Examples for Exercise on the Globes.

1. What day of the year is of the same length as the
14th of August?

2. How many miles make a degree of longitude in the
latitude of Lisbon ?

3. At what hour is the sun due east at London on the
5th of May ?

4. There is a place in the parallel of 31 deg. of north
latitude, which is 31 deg. distant from London ; what
place is it ?

5. If the sun's meridian altitude at London be 30 deg.,
what day of the month, and what month, is it ?

336 A PROMISCUOUS COLLECTION Part IV.

6. On what month and day is the sun's meridian alti-
tude at Paris equal to the latitude of Paris ?

7. When y Draconis is vertical to the inhabitants of
London at 10 o'clock at night ; what day of the month,
and what month, is it ?

8. What is the equation of time dependent on the ob-
liquity of the ecliptic on the 14th of July?

9. I observed the pointers in the Great Bear, on the
meridian of London, at eleven o'clock at night ; in what
month, and on what night, did this happen ?

10. On what day of the month, and in what month,
will the shadow of a cane placed perpendicular to the
horizon of London, at ten o'clock in the morning, be
exactly equal in length to the cane ?

11. The earth goes round the sun in 365 days 6 hours
nearly ; how many degrees does it move in one day, at
a medium,? Or, what is the daily apparent mean motion
of the sun ?

12. The moon goes once round her orbit, from the
first point of the sign Aries to the same again, in 27 days
7 hours 4-3 minutes 5 seconds ; what is her mean motion
in one day?

13. The moon turns round her axis, from the sun to
the sun again, in 29 days 12 hours 44 minutes 3 seconds,
which is exactly the time that she takes to go round her
orbit from new moon to new moon ; at what rate per hour
are the inhabitants (if any) of her equatorial parts
carried by this rotation, the moon's diameter being
21 44 miles?

14. How many degrees does the motion of the moon
exceed the apparent motion of the sun in 24 hours ?

15. Find on what day, in any given month, the moon
is eight days old, and then find her longitude for that
day.

16. Travelling in an unknown latitude I found, by
chance, an old horizontal dial ; the hour-lines of which
were so defaced by time that I could only discover those
of IV. and V., and found their distance to be exactly
21 degrees ; pray, what latitude was the dial made for ?

17. Required the duration of twilight at the south
pole ?

Chap. I. OF EXERCISES ON THE GLOBES. 337

18. How far must an inhabitant of London travel
southward to lose sight of Aldebaran ?

19. What is the elevation of the north polar star above
the horizon of Calcutta ?

20. Lord Nelson beat the French fleet near latitude
31 deg. 11. min. north, longitude 30 deg. 22min. east;
point out the place on the globe ?

21. What is the sun's altitude at three o'clock in the
afternoon at Philadelphia on the 7th of May ? i

22. What is the length of the day at London on the
26th of July, and how many degrees must the sun's
declination be diminished to make the day an hour
shorter ?

23. At what hour does the sun first make his appear-
ance at Petersburgh on the 4th of June ?

24. At what rate per hour are the inhabitants of
Botany Bay carried from west to east by the rotation of
the earth on its axis?

25. When Arcturus is 30 deg. above the horizon of
London, and eastward of the meridian, on the 5th of
November, what o'clock is it ?

26. Describe an horizontal dial for the latitude of
Washington ?

27. Describe a vertical dial facing the south for the
latitude of Edinburgh ?

28. What is the moon's greatest altitude to the in-
habitants of Dublin ?

29. What is the sun's greatest altitude at the southern
extremity of Patagonia ?

30. At what hour at London, on the 15th of August,
will the Pleiades be on the meridian of Philadelphia ?

31. If a comet, whose longitude was 4 signs 5 deg.,
and latitude 44 deg. north, appeared in Ursa Major, in
what part of the constellation was it ?

32. On what point of the compass does the sun set at
Madrid, when constant twilight begins at London ?

33. What is the difference between the duration of
twilight at Petersburgh and Calcutta, on the first of
February ?

34. How much longer is the 10th of December at
Madras than at Archangel ?

338 A PROMISCUOUS COLLECTION Part IV,

35. How much longer is the 5th of May at Archangel
than at Madras ?

36. When it is two o'clock in the afternoon at London,
on the 15th of February, to what places is the sun rising
and setting, and where is it noon ?

37. Whether does the sun shine over the north or south
pole on the 17th of April, and how far ?

38. At what hour on the 18th of April will the sun's
altitude, and azimuth from the east towards the south, be
each 40 deg. at London ?

39. Which way must a ship steer from Rio Janeiro to
the Cape of Good Hope ?

40. Are the clocks at Philadelphia faster or slower than:
those at London, and how much ?

41. Are the clocks at Calcutta faster or slower than the
clocks at London, and how much ?

42. What is the difference of latitude between Copen^
hagen and Venice?

43. There is a place in latitude 31 deg. 11 min. north,
situatec}, by an angle of position, south-east by east \ east
from London ; what place is that, and how far is it from
London in English miles ?

44. On the 6th of October, 1844, the right ascension
of Venus will be 9 deg. 56 min., declination 11 deg. 37 min.
north ; will Venus rise before or after the sun, and how
much?

45. On the 9th of September, 1845, the right ascension
of Venus will be 13 deg. 5 min., declination 6 deg. 30
min. south; will Venus rise before or after the sun, and
how much ?

46. On the 26th of December, 1845, the right ascension
of the planet Jupiter will be 1 deg. 57 min., declination
10 deg. 37 min. north ; at what hour will he rise, come to
the meridian, and set at London ?

47- On the 1st of January, 1846, the moon's right
ascension at noon will be 22 hrs. 4 min., declination 6 deg.
39 min. south ; required her setting amplitude at London,
and the hour and azimuth, when she is 25 deg. above the
horizon ?

48, The moon's right ascension on the 5th of November,
1845, at midnight, will be 20 hrs. 18 min., decimation

Chap. I. OF EXERCISES ON THE GLOBES. 339

14 deg. 23 min. south ; required the time of her rising,
coming to the meridian, and setting at London, and the
time of high water at London Bridge ?

49. To what places of the earth will the moon be ver-
tical on the 7th of February, 1845, her right ascension at
midnight being 12 hrs. 11 min., and declination 6 deg.
50 min. south ?

50. On the 1st of January, 1845, the moon's ascending
node will be 8 signs 12 deg. 52 min. ; where will the de-
scending node be ?

51. The moon's declination at midnight, on the 1st of
November, 1845, will be 16 deg. 18 min. south ; to what
places of the earth will she be vertical ?

52. What stars are constantly above the horizon of
Copenhagen ?

53. I observed the altitude of Betelgeux to be 19 deg.,
and that of Aldebaran 40 deg. ; they both appeared in
the same azimuth, viz. exactly east; what latitude was
I in?

54. In what latitude is Aldebaran on the meridian when
/3 in the Lion's tail is rising ?

55. In what latitude is Rigel setting when Regulus is on
the meridian ?

56. In what latitude are the pointers in the Great Bear
on the meridian when Vega is rising ?

57. In latitude 79 deg. north, on the 1st of February,
at what hour will Procyon and Regulus have the same al-
titude ?

58. At what hour on the 10th of February will Capella
and Procyon have the same azimuth at London ?

59. On the 10th of November at eight o'clock in the
evening, Bellatrix in the left shoulder of Orion was rising :
what was the latitude of the place ?

60. On the 16th of February, Arcturus rose at eight
o'clock in the evening ; what was the latitude ?

61. At what hour of the night, on the 16th of February,
will the altitude of Regulus be 28 deg. at London?

62. Required the altitude and azimuth of Markab in
Pegasus, at London, on the 21st of September, at nine
o'clock in the evening ?

63. On what day of the month, and in what month, will

Q 2

340 A PROMISCUOUS COLLECTION Part IV.

the pointers of the Great Bear be on the meridian of Lon-
don at midnight ?

64. What inhabitants of the earth have the greatest
portion of moonlight ?

65. On what day of the year will Altai r, in the Eagle,
come to the meridian of London with the sun ?

66. In what latitude north is the length of the longest
day eleven times that of the shortest ?

67. In what latitude south is the longest day eighteen
hours?

68. At what time does the morning twilight begin, and
what time does the evening twilight end, at Philadelphia,
on the 15th of January?

69. When it is four o'clock in the afternoon at London,
on the 4th of June, where is it twilight?

70. Required the antipodes of Cape Horn ?

71. Required the perioeci of Philadelphia ?

72. Required the antceci of the Sandwich Islands ?

73. What is the angle of position between London and
Jerusalem ?

74. Required the nearest distance between London and
Alexandria, in English and in geographical miles ?

75. In what latitude north does the sun begin to shine
constantly on the 10th of April?

76. How long does the sun shine without setting
at the north pole; and what is the duration of dark
night ?

77. Where is the sun vertical when it is midnight at
Dublin on the 15th of July ?

78. When it is five o'clock in the evening at Philadel-
phia, where is it midnight, and where is it noon ?

79. What places have the same hours of the day as
Edinburgh ?

80. What places have opposite hours to the respective
capitals of Europe ?

81. At what hour at London is the sun due east at the
time of the equinoxes ?

82. At what hour at London is the sun due east at the
time of the solstices ?

83. In what climates are the following places situated,

Chap, I. OF EXERCISES ON THE GLOBES. 341

viz. Philadelphia, Madrid, Drontheim, Trincomale', Cal-
cutta, and Astracan ?

84. On what day of the year does Regulus rise helia-
cally at London ?

85. On what day of the year does Betelguex set helia-
cally at London ?

86. What stars set acronically at London on the 24th
of December?

87. What stars rise acronically at London on the 12th
of December ?

88. In what latitude north do the bright stars in the
head of the Dolphin and Altair in the Eagle, rise at the
same hour ?

89. In what latitude north do Capella and Castor set at
the same hour, and what is the difference of time between
their coming to the meridian ?

90. What stars rise cosmically at London on the 7th of
December ?

91. What stars set cosmically at London on the 10th
of December ?

92. What degrees of the ecliptic and equinoctial rise
with Aldebaran at London ?

93. On what day of the year does Arcturus come to the
meridian of London, at two o'clock in the morning ?

94. On what day of the year does Regulus come to the
meridian of London, at nine o'clock in the evening?

95. At what time does Vega in Lyra come to the me-
ridian of London, on the 1 8th of August?

96. Trace out the galaxy or milky-way on the celestial
globe.

97. If the meridian altitude of the sun on the 7th of
June be 50 deg., and south of the observer, what is the
latitude of the place ?

98. Required the sun's right and oblique ascension at
London at the equinoxes ?

99. Required the sun's right ascension, oblique ascen-
sion, ascensional difference, and time of rising and setting
at London, on the 5th of May ?

100. If the sun's rising amplitude on the 7th of June
be 24 deg. to the northward of the east, what is the lati-
tude of the place ?

Q 3

34-2 A PROMISCUOUS COLLECTION Part IV.

101. What stars have nearly the following degrees of
right ascensions and decimations ?

7° 10' R.A. 29° 45' D.N. II 162° 49' R.A. 62° 50' D.N.

14 38 R.A. 34 33 D.N. 244 17 R.A. 25 58 D.S.

135 59 R.A. 3 10 D.N. | 238 27R.A. 19 15 D.S.

102. Describe an horizontal sun-dial, for the latitude of
Edinburgh ?

103. What is the length of the day on February 14th at
London, and how much must the sun's declination de-
crease to make the day an hour longer ?

104. What hour is it at London when it is 17 minutes
past 4 in the evening at Jerusalem ?

105. On the 21st of June the sun's altitude was ob-
served to be 46 deg. 25 min., and his azimuth 112 deg
59 min. from the north towards the east, at London ; what
was the hour of the day ?

106. Given the sun's declination 17 deg. 2 min. north,
and increasing ; to find the sun's longitude, right ascen-
sion, and the angle formed between the ecliptic and the
meridian passing through the sun ?

107. Given the sun's right ascension 225 deg. 18 min.
to find his longitude, declination, and the angle formed
between the ecliptic and the meridian passing through the

sun

108. Given the sun's longitude 26 deg. 9 min. in & ;
to find his declination, ri^ht ascension, and the angle
formed between the ecliptic and the meridian passing
through the sun ?

109. Given the sun's amplitude 39 deg. 50 min. from
the east towards the north, and his declination 23| deg.
north ; to find the latitude of the place, the time of the
sun's rising and setting, and the length of the day and
night ?

110. At what time on the 1st of April will Arcturus
appear upon the 6 o'clock hour-line at London, and what
will his altitude and azimuth be at that time ?

111. Required the altitude of the sun, and the hour he
will appear due east at London, on the 20th of May ?

112. At what hours will Arcturus appear due east and
west at London, on the 2d of April, and what will its alti-
tude be ?

Chap. I. OP EXERCISES ON THE GLOBES* 34-3

113. At London, the sun's altitude was observed to be
25 deg. 30 min. when on the prime vertical ; required his
declination, and the hour of the day ?

1 14-. On the 12th of April, 1845, the moon's right ascen-
sion at midnight will be 6 hrs. 10 min., and her declination
20 deg. 20 min. north ; required her distance from Regulus,
Procyon, and Betelguex, at that time ?

115. The distance of a comet from Sirius was observed
to be 66 deg., and from Procyon 51 deg. 6 min. ; the
comet was westward of Sirius ; required its latitude and
longitude ?

116. Find the Golden Number, the Epact, Sunday
Letter, the Number of Direction, the Paschal full moon,
and Easter day, for the years 184-3, 1844, and 1845, dis-
tinguishing the leap years.

117. The declination of y in the head of Draco is 5 1 deg.
30 min. north ; to what places will it be vertical when it
comes to their respective meridians ?

118. When is it four o'clock in the evening at London
on the 4th of May, to what places, is the sun rising and
setting, where is it noon and midnight, and to what place
is the sun vertical ?

119. At what time does the sun rise and set at the
North Cape, on the north of Lapland, on the 5th of April,
and what is the length of the day and night ?

120. At what time does the sun rise at the Shetland
Islands when it sets at four o'clock in the afternoon at
Cape Horn ?

121. Walking in Kensington Gardens on the 17th of
May, it was 12 o'clock by the sun-dial, and wanted
eight minutes to twelve by my watch; was my watch
right ?

122. If the sun set at nine o'clock, at what time does
it rise, and what is the length of the day and night ?

123. Where is the sun vertical when it is five o'clock
in the morning at London on the 15th of May ?

124. At what hour does day break at London on the
5th of April ?

125. If the moon should be 22 days old on the 27th of
June, 1845, at what time will she rise, culminate, and set
at London ?

344 A PROMISCUOUS COLLECTION Part IV.

126. On what day of the month, and in what month,
does the sun rise 24 deg. to the north of the east at
London ?

127. When the sun is rising to the inhabitants of
London on the 8th of May, where is it setting ?

128. When the sun is setting to the inhabitants of
Calcutta on the 18th of March, where is it midnight?

129. What is the difference between the circumference
of the earth at the equator and at Petersburg, in English
miles ?

130. At what hour does the sun rise at Barbadoes when
constant twilight begins at Dublin ?

131. When the sun is rising at O Vhy'hee on the 18th
of May, where is it noon ?

132. At what hour does the sun rise at London when
it sets at seven o'clock at Petersburg!! ?

133. How high is the north polar star above the horizon
of Quebec?

134. How many English miles must an in-
habitant of London travel southward, that the me-
ridian altitude of the north polar star may be diminished
25 deg. ?

135. How many English miles must I 'sail or travel
westward from London that my watch may be seven
hours too fast ?

136. What place of the earth has the sun in the zenith,
when it is seven o'clock in the morning at London, on the
25th of April?

137. On what day of the month, and in what month,
is the sun's amplitude at London equal to one third of the
latitude ?

138. On what month and day is the sun's amplitude
at London equal to the latitude of Kingston, in
Jamaica ?

139. If the moon foe 25 days old on the 3d of April,
1 845, what is her longitude ?

140. If the highest point of Mont Blanc be 5101 yards
above the level of the sea, what would be its altitude on a
globe of 18 inches in diameter?

141. If the polar diameter of the earth be to the equa^
torial diameter as 229 is to 230, what would the polar

Chap. I. OF EXERCISES ON THE GLOBES. 345

diameter of a three-inch globe be, if constructed on this
principle ?

142. What inhabitants of the earth, in the course of
12 hours, will be in the same situation as their antipodes?

143. On what day of the year at London is the twilight
eight hours long ?

144. At what time does the sun rise and set at London,
when the inhabitants of the north pole begin to have dark
night ?

145. At what hour does the sun set at the Cape of
Good Hope, when total darkness ends at the north
pole?

146. What is the moon's longitude if full moon happens
on the 22d of April, 1845?

147. Does the sun ever rise and set at the north pole ?

148. At what hour of the day, on the 15th of April,
will a person at London have his shadow the shortest
possible ?

149. If the precession of the equinoxes be 50! seconds
in a year, how many years will elapse before the constel-
lation Aries will coincide with the solstitial colure ?

150. If the obliquity of the ecliptic should continually
diminish at the rate of 0*457 seconds in a year, as stated
by Bessel, how many years will elapse from the 1st of
January, 1845, when the obliquity of the ecliptic will be
23 deg. 27 min. 34-23 sec., before the ecliptic will coin-
cide with the equinoctial ?

151. Required the duration of dark night at the south
of Nova Zembla ?

152. When constant twilight ends at Petersburgh, where
is the day 18 hours long ?

153. At what hour does the sun set at Constantinople,
when it rises 12 deg. to the north of the east?

154. What is the difference between a solar and a side-
real year, and what does that difference arise from ?

155. What is the difference between the length of a
natural or astronomical day and a sidereal day, and how
does the difference arise ?

156. Required the difference between the length ot
the longest day at Cape Horn and at Edinburgh ?

157. If one man were to travel eight miles a day west-

Q 5

346 A PROMISCUOUS COLLECTION, &c. Part IV.

ward round the earth at the equator, and another two
miles a day westward round it in the latitude of 80 deg.
north ; in how many days would each of them return to
the place whence he set out ?

158. If a pole of 18 feet in length be placed perpen-
dicular to the horizon of London on the 15th of July, and
another exactly of the same length be placed in a similar
manner at Edinburgh, which will cast the longer shadow
at noon ?

159. If the moon be in 29 deg. of Leo at the time of
new moon, what sign and degree will she be hi when she
ia five days old ?

160. What is the duration of constant day or twilight
at the north of Spitzbergen ?

161. What place upon the globe has the greatest
longitude, the least longitude, no longitude, and every
longitude ?

162. In what latitude is the length of the longest clay,
to the length of the shortest, in the ratio of 3 to 2 ?

163. If a man of 6 feet high were to travel round the
earth, how much farther would his head go than his feet ?

164. On what day of the week will the 10th of Janu-
ary fall in the year 1845 ?

165. At what hour, in the afternoon, London time, on
the 21st of June, will the shadow of a pole 10 feet high
at Barbadoes, be the same length as the meridional
shadow of a similar pole at London on the same day?

166. One end of a wall declines 30 degrees from the
east towards the north, and the other end 60 degrees from
the south towards the west in latitude 51° 30' N., at what
hour on the 21st of June does the sun begin to shine on
the south of the wall, and at what hour does it leave it ?

167. The south wall of a church declines 12° 30/ to-
wards the east, in latitude 52° N., against which a vertical
dial is fixed ; for how many hours will the sun shine upon
that dial on the 10th of May?

168. A clock, with a pendulum that beats seconds, and
kept true time on the surface of the earth, was carried to
the top of a mountain, and there lost 3 seconds in an hour,
what was the. height of the mountain ?

Chap. II. QUESTIONS FOR THE EXAMINATION, &C. 34?

CHAPTER II.

A Collection of Questions, with References to the Pages
where the Answers will be found; designed as an As-
sistant to the Tutor* in the examination of the Student.

1. How many kinds of artificial globes are there?

2. What does the surface of the terrestrial globe re-
present, and which way is its diurnal motion ? (page 1.)

3. What does the surface of the celestial globe ex-
hibit, which way is its diurnal motion, and where is the
student supposed to be situated when using it ?

I. GREAT CIRCLES ON THE TERRESTRIAL* GLOBE*.

1. What is a GREAT CIRCLE, and how many are there
drawn on the terrestrial globe ? (Definition 6, page 3.)

2. What is the equator, and what is its use ? (Def. 10.
page 3.)

3. What are the meridians, and how many are drawn oa
the terrestrial globe ? (Def. 8, page 3.)

4. What is the first meridian ? (Def. 9, page 3.)

5. What is the ecliptic, and where is it situated ? (Def.
11, page 3.)

6. What are the colures, and into how many parts do
they divide the ecliptic ? (Def. 14, page 5.)

7. What are the hour-circles, and how are they drawn
on the globe? (Def. 50, page 12.)

8. What hour-circle is called the six o'clock hour-line ?
(Def. 51, page 12.)

9. What are the azimuth or vertical circles, and what
is their use ? (Def. 43, page 11.)

10. What is the prime vertical ? (Def. 44, page 11.)

* Though a reference be given to the pages where the answers to
each question maybe found; yet, perhaps, it would be better for the
student not to learn the answers by heart, verbatim from the book ; but
to frame an answer himself, from an attentive perusal of his lesson :
by which means the understanding will be called into exercise as w<
as the memory.

Q 6

348 QUESTIONS FOR THE EXAMINATION Part IV.

II. SMALL CIRCLES ON THE TERRESTRIAL GLOBE.

1. What is a SMALL CIRCLE, and how many are gene-
rally drawn on the terrestrial globe ? (Def. 7, page 3.)

2. What are the tropics, and how far do they extend
from the equator, &c.? (Def. 16, page 5.)

3. What are the polar circles, and where are they situ-
ated? (Def. 17, page 5.)

4. What are the parallels of latitude, and how many
are generally drawn on the terrestrial globe? (Def. 18,
page 6.)

5. What circles are called Almacanters? (Def. 40,
page 11.)

III. GREAT CIRCLES ON THE CELESTIAL GLOBE.

1 . How many GREAT CIRCLES are drawn on the celes-
tial globe?

2. The lines of terrestrial longitude are perpendicular
to the equator, on the terrestrial globe, and all meet in
the poles of the world ; to what great circle on the globe
are the lines of celestial longitude perpendicular, and on
what points of the globe do they all meet ?

3. What are the colures, and into how many parts do
they divide the ecliptic ? (Def. 14, page 5.)

4. What is the equinoctial, and what is its use ? (Def.

10, page 3.)

5. What is the ecliptic, and where is it situated ? (Def.

11, page3.)

6. What is the zodiac, and into how many parts is it
divided? (Def, 12, page 4.)

7. What are the signs of the zodiac, and how are they
marked ? (Def. 13, page 4.)

8. Which are the spring, summer, autumnal, and winter
signs ; and on what days does the sun enter them ? (Def.
13, pageS.)

9. Which are the ascending and descending signs ?
13, page 4.)

Chap. II. OF THE STUDENT. 34,9

IV. SMALL CIRCLES ON THE CELESTIAL GLOBE.

1. How many SMALL CIRCLES are drawn on the celes-
tial globe ?

2. What are the tropics, and how far do they extend
from the equinoctial ? (Def. 16, page 5.)

3. What are the polar circles, and where are they situ-
ated? (Def. 17, page 5.)

4. What are the parallels of celestial latitude ? (Def.
41, page 11.)

5. What are the parallels of declination ? (Def. 42,
page 11.)

V. THE BRASS MERIDIAN, AND OTHER APPENDAGES TO
THE GLOBES.

1. What is the brazen meridian, and how is it divided
and numbered ? (Def. 5, page 2.)

2. What is the axis of the earth, and how is it repre-
sented by the artificial globes ? (Def. 3, page 2.)

3. What are the poles of the world ? (Def. 4, page 2.)

4. What are the hour-circles, and how are they divided?
(Def. 19, page 6.)

5. What is the horizon, and what is the distinction be-
tween the rational and sensible horizon? (Def. 20, 21, and
22, pages 6 and 7.)

6. What is the wooden horizon, and how is it divided ?
(Def. 23, page 7.)

7. What is the mariner's compass, how is it divided,
and what is the use of it on the globe? (Def. 33, 34, and
note page 9.)

8. What is the quadrant of altitude, how is it divided,
and what is its use ? (Def. 37, page 10.)

VI. POINTS ON, AND BELONGING TO, THE GLOBES.

1. What is the pole of a circle? (Def. 29, page 8.)

2. What is the zenith, and of what circle is it the pole.'1
(Def. 27, page 8.)

350 QUESTIONS FOR THE EXAMINATION Part IV.

3. What is the nadir, and of what circle is it the pole ?
(Def. 28, page 8.)

4. What are the cardinal points of the horizon ? (Def.

24, page 8.)

5. What are the cardinal points in the heavens ? (Def.

25, page 8.)

6. What are the cardinal points of the ecliptic, and
which are the cardinal signs ? (Def. 26, page 7.)

7. What are the equinoctial points ? (Def. 30, page 8.)

8. What are the solstitial points ? (Def. 31, page 8.)

9. What is the culminating point of a star, or of a
planet? (Def. 52, page 13.)

10. What are the poles of the ecliptic, how far are they
from the poles of the world, and in what circles are they
situated ? (Def. 29, page 8.)

VII. LATITUDE AND LONGITUDE ON THE TERRESTRIAL
GLOBE, THE DIVISION OF THE GLOBE INTO ZONES AND
CLIMATES, THE POSITIONS OF THE SPHERE, THE SHA-
DOWS AND POSITIONS OF THE INHABITANTS WITH RE-
SPECT TO EACH OTHER.

L What is the latitude of a place on the terrestrial
globe? (Def. 35, page 10.)

2. What is the longitude of a place on the terrestrial
globe? (Def. 38, page 10.)

3. What is a zone, and how many are there on the ter-
restrial globe ? (Def. 70, page 19.)

4. What is the situation, and what is the extent of the
torrid zone ? (Def. 71, page 20.)

5. Where are the two temperate zones situated, and
what is the extent of each ? (Def. 72, page 20.)

6. Where are the two frigid zones situated, and what is
the extent of each ? (Def. 73, page 20.)

7. What is a climate, and how many are there on the
globe? (Def. 69, page 17.)

8. Have all places in the same climate the same atmo-
spherical temperature ? (Note, page 17.)

9. How many different positions of the sphere are
there ? (Def. 65, page 16.)

10. Wliat is a right sphere, and what inhabitants of

II. OF THE STUDENT. 351

the globe have this'position ? (Def. 66, page 16; see like-
wise Prob. XXII. page 217.)

11. What is a parallel sphere, and what inhabitants of
the globe have this position? (Def. 67 , page 16; and
Prob. XXII. page 218, &c.)

12. What is an oblique sphere, and what inhabitants
of the globe have this position ? (Def. 68, page 17 ; and
Prob. XXII. page 220, &c.)

13. What parts of the globe do the AMPHISCII inhabit,
and why are they so called ? (Def. 74-, page 20.)

14. When do the AMPHISCII obtain the name of
ASCII ?

15. What parts of the globe do the HETEROSCII inha-
bit, and why are they so called ? (Def. 75, page 20.)

16. What parts of the globe do the PERISCII inhabit,
and why are they so called? (Def. 76, page 20.)

17. What inhabitants are called ANTOECI to each
other, and what do you observe with respect to their
latitudes, longitudes, hours, &c. ? (Def. 77, page 21.)

18. What inhabitants are called PERIOECI to each other,
and what is observed with respect to their latitudes, longi-
tudes, hours, seasons, &c. ? (Def. 78, page 21.) ^

19. What are the ANTIPODES, and what is observed
with respect to their seasons of the year, &c. ? (Def. 79,
page 21.)

VIII. LATITUDES AND LONGITUDES OF THE STARS AND
PLANETS ON THE CELESTIAL GLOBE, &C. TOGETHER
WITH THE POETICAL RISING AND SETTING OF THE
STARS, &C.

1. What is the latitude of a star or planet? (Def. 36

2. What is the longitude of a star or planet ? (Def. 39
page 11.)

3. What are the fixed stars, and why are they so
called? (Def. 89, page 25.)

4. What is a constellation, and how many are there on
the celestial globe ? (Def. 91, page 26; see the tablet,
pages 27, 28, and 29.)

352 QUESTIONS FOR THE EXAMINATION Part IV.

5. What is meant by the poetical rising and setting of
the stars? (Def. 90, page 26.)

6. When is a star said to rise and set cosmically?

7. When is a star said to rise and set acronically ?

8. When is a star said to rise and set heliacally ?

9. What is the Via Lactea, and through what constel-
lations does it pass ? (Def. 92, page 36.)

10. What kind of stars are termed nebulous ? (Def. 93,
page 37.)

11. How are the stars, which have not particular
names, distinguished on the celestial globe ? (Def. 94-,
page 37.)

JX. DEFINITIONS AND TERMS COMMON TO BOTH THE
GLOBES.

1. What is the decimation of the sun or star, or planet?
(Def. 15, page 5.)

2. What is an hemisphere ? (Def. 32, page 8.)

3. What is the altitude of any object in the heavens ?
(Def.te, page 11.)

4. What is the meridian altitude of the sun, a star, .or
planet ?

5. What is the zenith distance of a celestial object ?
(Def. 46, page 11.)

6. What is the polar distance of a celestial object ?
(Def. 47, page 12.)

7. What is the amplitude of a celestial object ? (Def.

48, page 12.)

8. What is the azimuth of a celestial object? (Def.

49, page 12.)

9. What is the right ascension of the sun, or of a star,
&c.? (Def. 80, page 21.)

10. What is the oblique ascension of the sun, or of a
star, &c. ? (Def. 81, page 21.)

11. What is the oblique descension of the sun, or of a
star, &c.? (Def. 82, page 21.)

12. What is the ascensional or descensional difference?
(Def. 83, page 21.)

II. OF THE STUDENT. 353

X. TIME; YEARS, DAYS, &c.

1. What is a solar or tropical year, and what is the
length of it? (Def. 62, page 15.)

2. What is a sidereal year, and what is its duration ?
(Def. 63, page 15.)

3. What is an astronomical day ? (Def. 58, page 14.

4. What is a mean solar day ? (Def. 57, page 13.)

5. What is a true solar day ? (Def. 56, page 13.)

6. What is an artificial day ? (Def. 59, page 14.)

7. What is a civil day ? (Def. 60, page 14.)

8. What is ^sidereal day? (Def. 61, page 14.)

9. What is meant by apparent noon, or apparent time ?
(Def. 53, page 13.)

10. What is true or mean noon? (Def. 54, page 13.)

11. What is the equation of time at noon? (Def. 55,
page 13.)

12. What is the calendar ? (page 178.)

13. WTiat is the cycle of the moon, and how is it found?
(page 178.)

14. What is the epact, what is its use, and how is it
found? (page 179.)

15. What is the cycle of the sun, how is it found, arid
to what use is it applied ? (page 180.)

16. What is the number of direction, and how is Easter
found by it? (page 181.)

17. How do you find the Paschal full moon and Easter
by the epact ? (page 182.)

18. In how m^ny years will the error in the Gregorian
calendar amount to one day? (page 183.)

19. In what manner do you find the moon's age, the
time of new moon, and the time of full moon, by the table
page 184?

XI. ASTRONOMICAL AND MISCELLANEOUS
DEFINITIONS, &C.

1. What do you understand by the precession of the
equinoxes, and in what time do they make an entire re-
volution round the equinoctial ? (Def. 64, page 15.)

354; QUESTIONS FOR THE EXAMINATION Part IV.

2. What is the crepusculum or twilight, and what is the
cause of it? (D/.84, page 21.)

3. What is refraction, and whence does it arise ? (Def.
85, pages 22, 23, and 24.)

4. What is meant by the parallax of the celestial
bodies ? (Def. 86, page 24.)

5. What is an angle of position between two places ?
(Def. 87, page 25 ; and note, pages 199 and 200.)

6. What are rhumbs and rhumb-lines ? (Def. 88,
page 25.)

7. What are the planets, and how many belong to the
solar system ? (Def. 95, page 38.)

8. What is the distinction between primary and se-
condary planets, and how many secondary planets belong
to the solar system ? (Def. 96 and 98, pages 38 and 39.)

9. What is the orbit of a planet ? (Def. 99, page 39.)
Of what figure are the orbits of the planets, and in what
part of the figure is the sun placed ? (page 143.)

10. What are the nodes of a planet? (Def. 100, page
39.)

11. What are the different aspects of the planets, and
how many are there ? (Def. 10l> page 39.)

12. What the syzygies and quadratures of the moon ?

13. When is a planet's motion said to be direct, sta-
tionary, or retrograde ? (Def. 102, 103, and 104, page 39.)

14. What is a digit ? (Def. 105, page 39.)

15. What is the disc of the sun or moon ? (Def. 106,
page 39.)

16. What are the geocentric and heliocentric latitudes
and longitudes of the planets? (Def. 107 and 108, page
40.)

17. When is a planet said to be hi apogee ? (Def. 109,
page 40.)

18. When is a planet said to be in perigee ? (Def. 110,
page 40.)

19. What is the aphelion or higher apsis of a planet's
orbit? (Def. Ill, page 40.)

20. What is the perihelion or lower apsis of a planet's
orbit? (Def. 112, page 40.)

21. What is the line of the apsides? (Def. 113, page
40.)

Chap. II. OF THE STL DENT. 355

22.* What is the eccentricity of the orbit of a planet?
(Def. 114, page 40.)

23. What is the elongation of a planet? (Def. 119,
page 40.)

24. What are the occultation and transit of a planet ?
(Def. 115 and 116, page 40.)

25. What is the cause of an eclipse of the sun ? (Def.

117, page 40.)

26. What is the cause of an eclipse of the moon ? (Def.

118, page 40.)

27. What are the nocturnal and diurnal arcs described
by the heavenly bodies ? (Def. 121, and 120, page 41.)

28. What is the aberration of a star ? (Def. 122, page

29. What are the centripetal and centrifugal forces?
(Def. 123 and 124, page 42.)

30. What is gravity ? (Def. 8, page 48.)

31. What is the vis inertias of a body? (Def. 9, page
48.)

32. What is matter, and what are its general proper-
ties ? (Def. 1 and 2, page 46.)

33. What are extension, figure, and solidity ? (Def. 3,
4, and 5, page 46.)

34. Can matter be divided ad infiftitum? (Def. 7,
page 47.)

35. What is motion, and what is the distinction be-
tween absolute and relative motion ? (Def. 6, page 47 ; and
Def. 10, page 49.)

36. How is the velocity of a body measured, and what
do you understand by the word force? (Def. 11 and 12,
page 49.)

37. What are Sir I. Newton's three laws of motion ?
(pages 49 and 50.)

38. What is compound motion ? (page 51 to 56.)

XII. THE SOLAR SYSTEM AND THE SUN 0.

1. What is the solar system, and why is it so called r
(page 141.)

2. What part of the solar system is caljed the centre of
the world ? (page 142 )

356 QUESTIONS FOR THE EXAMINATION Part IV.

3. Does not the sun revolve on its axis, and what other
motion has it ? (page 141.)

4. Of what shape is the sun, how far is it from the
earth, and how many miles is it in diameter ? (page 142.)

5. What is the comparative magnitude between the
sun and the earth ? (page 142.)

XIII. OF MERCURY $ .

1. What is the length of Mercury's year? (page 144«)

2. What is the greatest elongation of Mercury ?

3. What is the distance of Mercury from the sun ?

4. What is the diameter of Mercury ? (page 145.)

5. What is the comparative magnitude between Mer-
cury and the earth ?

6. What is the comparison between -the light and heat
which Mercury receives from the sun, and the light and
heat which the earth receives ? (page 145.)

7. At what rate per hour are the inhabitants of Mer-
cury (if any) carried round the sun ? (page 146.)

XIV. OF VENUS ?.

1. When is Venus an evening star, and in what situ-
ation is she a morning star ? (page 146.)

2. How long is Venus a morning star ? (page 147.)

3. In how many days does Venus revolve round the
sun?

4. The last transit of Venus over the sun's disc hap-
pened in 1769, when will the next transit happen ?

5. What is the opinion of Dr. Herschel respecting the
mountains in Venus ? (page 148.)

6. What is the opinion of M. Schroeter on the same
subject? (page 157» in the note.)

7. What is the greatest elongation of Venus ? (page 148.)

8. What is the diameter of Venus ?

9. What is the magnitude of Venus ?

10. What is the distance of Venus from the sun?

11. What is the comparison between the light and heat

Chap II. OF THE STUDENT. 357

which Venus receives from the sun, and the light and
heat which the earth receives ?

12. At what rate per hour does Venus move round the
sun ? (page 149.)

XV. OF THE EARTH ®.

1. What is the figure of the earth? (page 57.)

2. Why is the earth represented by a globe ? (page 64-.)

3. What proofs have we that the earth is globular?
(pages 58, 59.)

4-. What would be the elevation of Chimbora9o, the
highest of the Andes mountains, on an artificial globe of
18 inches diameter? (page 59, the note.)

5. What is a spheroid, and how is it generated ? (page
59, the note.)

6. What is the difference between the polar and equa-
torial diameters of the earth? (page 61, and the note.)

7. What is the length of a degree ? (pages 62, 63, and
the note.)

8. What is the use of finding the length of a degree,
and how can the magnitude of the earth be determined
thereby ? (page 62.)

9. Who was the first person who measured the length
of a degree with tolerable accuracy ? (page 63.)

10. What is the length of a degree according to the
French admeasurement ? (page 63, the note.)

11. In what time does the earth revolve on its axis
from west to east ? (page 65, and Def. 61, page 14-, and
the note.)

1 2. What is the diameter of the earth ; what is its cir-
cumference, and how are they determined? (pages 62,
63, and the note.)

13. What proofs can you give of the diurnal motion of
the earth ? (pages 65 and 66.)

14. How do you explain the phenomena of the ap-
parent diurnal motion of the sun ? (page 66.)

15. What proofs can you. give of the annual motion
of the earth ? (page 67.)

16. What is the distance of the earth from the sun,
and how is it calculated? (page 68, and the note.)

358 QUESTIONS FOR THE EXAMINATION Part IV '.

17. At what rate per hour does the earth travel round
the sun ? (page 69.)

18. At what rate per hour are the inhabitants of the
equator carried from west to east by the revolution of the
earth on its axis, and at what rate per hour are the inha-
bitants of London carried the same way ?

19. How do you explain the motion of the earth round
the sun ? (page 70.)

20. How do you illustrate the phenomena of the dif-
ferent seasons of the year ? (page 71.)

XVI. OF THE MOON D .

1. How many kinds of lunar months are there ? (page
150.)

2. What is a periodical month ? (page 150.)

3. What is a synodical month ?

4. When is the eccentricity of the moon's elliptical
orbit the greatest? (page 150.)

5. When is the eccentricity of the moon's elliptical
orbit the least ? (page 150.)

6. Whether does the motion of the moon's node follow
or recede from the order of the signs ? (page 151.)

7. In how many years do the moon's nodes form a
complete revolution round the ecliptic? (page 151.)

8. In what time does the moon turn on her axis ?

9. What is the libration of the moon ?

1 0. Is the path of the moon convex or concave towards
the sun ? (page 152.)

11. Please to explain the different phases of the moon?
(pages 150 and 151.)

12. What point on the earth has a fortnight's moon-
light and a fortnight's darkness, alternately ? (pages 154
and 219.)

13. What is the moon's mean horizontal parallax, and
at what distance is she from the earth ? (page 154.)

14. What is the magnitude of the moon when compared
with that of the earth?

15. How many miles is the moon in diameter?

16. In how many days does the moon perform her re-

Chap. II. OF THE STUDENT. 359

volution round the earth, and at what rate does she travel
per hour ? (page 155.)

17. In what manner have astronomers described the
different spots on the moon's surface ?

18. Have not astronomers discovered volcanoes, moun-
tains, &c. in the moon ?

XVIL OF MARS <y.

1. What is the general appearance of Mars? (page
158.)

2. In what time does Mars revolve on his axis?

3. In what time does Mars perform his revolution
round the Kin, and at what rate does he travel per hour ?
(pages 158 and 159.)

4. How far is Mars distant from the sun? (page 159.)

5. How many miles is Mars in diameter ?

6. What is the comparative magnitude between Mars
and the earth ?

XVIII. OF CERES £, PALLAS $, JUNO f, AND VESTA Sf.

1. When and by whom was the planet or Asteroid
Ceres discovered ? (page 160.)

2. How many miles is Ceres in diameter ?

3. What is the distance of Ceres from the sun, and
what is the length of her year ?

4>. When and by whom was Pallas discovered ? (page
161.)

5. What is the diameter of Pallas in English miles ?

6. What is the distance of Pallas from the sun, and
the length of her year ?

7. Who discovered the planet Juno ? (page 160.)

8. How far is Juno distant from the sun, and what is
the length of her year ?

9. By whom was Vesta discovered?

10. What is the length of Vesta's year, anyhow far is
she from the sun ?

360 QUESTIONS FOR THE EXAMINATION Part IV.

XIX. OF JUPITER !(., &C.

1. In what situation is Jupiter a morning star, and in
what situation is he an evening star? (page 161.)

2. In what time does Jupiter revolve on his axis ?

3. What are Jupiter's belts ?

4. In what time does Jupiter perform his revolution
round the sun, and at what rate per hour does he travel ?
(page 162.)

5. What is the distance of Jupiter from the sun ?

6. What is the diameter of Jupiter in English miles ?

7. What is the comparative magnitude between Jupiter
and the earth ?

8. What is the comparison between the ligfct and heat
which Jupiter receives from the sun, and the light and heat
which the earth receives ? (page 162.),

9. How many satellites is Jupiter attended by ? (page
163.)

10. By whom were the satellites of Jupiter discovered?

11. In what time do the respective satellites perform
their revolutions round Jupiter ?

12. In what manner are the longitudes of places deter-
mined by the satellites of Jupiter? (page 164.)

13. Please to explain the configuration of the satellites
of Jupiter as given in the XlXth page of the Nautical
Almanac ?

14. How was the progressive motion of light discovered?
(page 165.)

XX. OF SATURN T2 , &C.

1. What is the appearance of Saturn when viewed
through a telescope ? (page 166.)

2. In what time does Saturn perform his revolution
round the sun, and at what rate does he travel per hour ?

3. What is the distance of Saturn from the sun ?

4. How many English miles is Saturn in diameter, and
what is his magnitude compared with that of the earth ?
(page 167.)

Chap. II. OF THE STUDENT 361

5. What is the comparison between the light and heat
which Saturn receives from the sun, and the light and heat
which the earth receives ?

6. In what time does Saturn revolve on his axis ?

7. How many moons is Saturn attended .by, and by
whom were they discovered ?

8. Pray is not the seventh satellite the nearest to
Saturn, and, if so, why was it not called the first satellite ?
(page 168.)

9. What is the ring of Saturn, and how may it be repre-
sented by the globe ? (page 169.)

10. By whom was the ring of Saturn discovered?

11* In what time does the ring of Saturn revolve round
the axis of Saturn ?

XXI. OF THE GEORGIAN PLANET $, &C.

1. When and by whom was the Georgian planet dis-
covered? (page 170.)

2. What is the appearance of the Georgian when viewed
through a telescope ? (page 170.)

3. In what time does the Georgian planet revolve round
the sun, and at what rate per hour does it travel ?

4. What is the comparative magnitude between the
Georgian planet and the Earth ?

5. How many satellites belong to the Georgian?

6. By whom were the satellites of the Georgian dis-
covered, and in what order do they perform their revolu-
tions round the planet ? (page 171 .)

N. B. The tutor may extend these questions to ttie Geographical Theo-
rems, page 42, to Chap. V. VI. VII. VIII. and IX. Part L, and
to Ckap. I. II. III. IV. and VI. Part IL / also to the manner of
solving the different problems, #c.

362

ETYMOLOGICAL TABLE

THE PRINCIPAL SCIENTIFIC TERMS

MADE USE OF IN THE FOflEGOING WORK .

BY THE EDITOR.

ABERRATION, from (Lat.) ab, from, and erro, to wander

Acronical, from (Greek) cc/cpov, a point, and ro£, night.

Aerolithes, from ( Greek) aTjp, air, and Xidos, a stone.

Altitude, from (Lat.) altitudo, height.

Amphiscii, from (Greek) ap^t, both, (mo, a shadow.

Antarctic, from (Greek) ami, opposite to, and op/troy, a bear.

Antipodes, from (Greek) curt, and TroSey, the feet-

Antoeci, from (Greek) avri, and oi/cew, to dwell.

Aphelion, from (Greek) OTTO, from, and r/Atoy, the sun.

Apogee, from ( Greek) cwro, and 717, the earth.

Apsis, from (Greek) cnj/*s, a bend, as of an arched roof, a ring, a

wheel, &c.

Arctic, from (Greek) apicros, a bear.

Ascii, from (Greek) a, not, or without, and tr/cta, a shadow.
Astronomy, from (Greek) affriqp, a star, and VO/JLOS, a law
Atmosphere, from ( Greek) aruos, vapour,, and atyatpa, a sphere.
Axis, from (Lat.) ago, to act.
Celestial, from (Lat.) ciclestis, heavenly.

Centrifugal, from (Lat.) centrum, the centre, andfugw, I flee.
Centripetal, from ( Lat. ) centrum, and peto, 1 seek.
Colure, from (Greek) Ko\ovpos, having the tail cut, mutilated.
Comet, from (Greek) KOJUT?, hair.

ETYMOLOGICAL TABLE. 3(33

Constellation, from (Lat.) con (for cum), with, and stella, a star.

Cosmical, from (Greek) icoo-fios, the world.

Dichotomised, from (Greek) SIX^TO/JLOS, cut into two parts.

Digit, from (Lat.) digitus, a finger.

Disc, from ( Greek) SICTKOS, a quoit.

Eccentricity, from (Greek) e/c, out of, and Kerrpov, centre.

Eclipse, from (Greek) eK\e«ro>, to faint away, or disappear.

Equinox, from (Lat.) eequus, equal, and nox, night.

Focus, from (Lat.)/ocws, afire-hearth.

Frigid, from (Lat.) frigidus, cold.

Geocentric, from (Greek) 777, the earth, and Kunpoy, the centre.

Gibbous, from (Lat.) gibbus, protuberant, hunched.

Gravity, from (Lat.) gratis, heavy.

Heliacal, from ( Greek) j)\ios, the sun.
Heliocentric, from (Greek) TJ\IOS, and K&npov, the centre.
Hemisphere, from (Greek) T)fj.i<rvs, half, and ffQaipa, a sphere.
Heterocsii, from ( Greek) eVepos, deviating from another, and ffKia, a

shadow.

Horizon, from ( Greek) 6pi$u, to limit.
Latitude, from (Lat.) latitude, breadth.
Longitude, from (Lat.) longitudo, length.
Matter, from (Lat.) materia (from mater, a mother).
Meridian, from (Lat.) men-dies, mid-day.
Node, from (Lat.) nodus, a knot.
Orbit, from (Lat.) orbita, a track.
Penumbra, from (Lat.) pene, almost, and umbra, a shade or

shadow.

Perigee, from ( Greek) Trepi, about, near, and TTJ, the earth.
Perihelion, from ( Greek) irepi, and ^Atos, the sun.
Perioaci, from (Greek) irepi, and otiteu, to dwell.
Periscii, from (Greek) -rrepi, and O-KIO, a shadow.
Phases, from (Greek) tyavis, appearances exhibited by any body in its

changes, as those of the moon.
Phenomenon, from ( Greek) ^aivofjiat, to appear.
Planet, from (Greek) ir\avr)Tr)s, wandering.
Satellite, from (Lat.) satelles, an attendant.
Sidereal, from (Lat.) sidus, a star.
Solar, from (Lat.) sol, the sun.
Solstice, from (Lat.) sol, and sisto, to stand.
Synceci, from (Greek) aw, with, together, oiKtu, to dwell.
Syssigies, from ( Greek) <rv(vyia, union.

364; ETYMOLOGICAL TABLE.

Terrestrial, from (Lat.) terrestris, earthly.

Torrid, from (Lat) torridus, hot.

Tropic, from (Greek) rpeiru, to turn.

Umbra, from (Lat.) umbra, a shade or shadow.

Vernal, from (Lat.) vernus, belonging to the spring.

Zodiac, from (Greek) £ca$iov, an animal.

Zone, from (Greek) Jtfnj, a girdle.

The following Words are of less perfect Etymology.

Alraacantar, from almokentor, a word partly Arabic and partly Greek,
and signifies a circle, having its centre in the same axis with
another.

Azimuth, from alsempt, an Arabic word, signifying the point or
mark.

Zenith and Nadir are also corruptions of two Arabic terms; the
iormer signifying a point, and applied to the vertical point, or
point over head, and the latter, the point opposite to the vertex.

THE END.

LONDON :

Printed by A. SPOTTISWOODB,
New- Street- Square.

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